Correct

Explanation: Median is the middle number when the data are ordered from least to greatest. In this case, there are 12 numbers, so, the median is the average of the middle two numbers, which are the 6th and 7th numbers in an ascending order. For the averaged high-temperature, the median is (56+60)/2=58, and for the averaged low-temperature, the median is (35+39)/2=37

Incorrect

The correct answer is high: 58F, low: 37F

Explanation: Median is the middle number when the data are ordered from least to greatest. In this case, there are 12 numbers, so, the median is the average of the middle two numbers, which are the 6th and 7th numbers in an ascending order. For the averaged high-temperature, the median is (56+60)/2=58, and for the averaged low-temperature, the median is (35+39)/2=37

Correct

Explanation: The volume of a sphere can be calculated from its radius as follows:

Incorrect

The correct answer is Q varies directly as the sixth power of W.

Explanation: The volume of a sphere can be calculated from its radius as follows:

Correct

Explanation: When we divide two polynomials with exponents, we subtract their exponents.

Incorrect

The correct answer E

Explanation: When we divide two polynomials with exponents, we subtract their exponents.

Correct

Explanation:

Incorrect

The correct answer is 66.7%

Explanation:

Correct

Explanation:

Incorrect

The correct answer is x=-1

Explanation:

Correct

Explanation: Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.

Incorrect

The correct answer is 2/7

Explanation: Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.

Correct

Explanation: Start by combining like terms.
4x + 5 = 13x + 4 – x – 9
4x + 5 = 12x – 5
–8x = –10
x = 5/4

Incorrect

The correct answer is 5/4

Explanation: Start by combining like terms.
4x + 5 = 13x + 4 – x – 9
4x + 5 = 12x – 5
–8x = –10
x = 5/4

Correct

Explanation: First we solve for x.
Subtracting 3 from both sides gives us –3x < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.

Incorrect

The correct answer is -6

Explanation: First we solve for x.
Subtracting 3 from both sides gives us –3x < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.

Correct

Explanation: The problem tells us that increasing x by twenty percent gives us the same thing that we would get if we decreased the product of four and x by five. We need to find expressions for these two situations, and then we can set them equal and solve for x.
Let's find an expression for increasing x by twenty percent. We could represent this as x + 20%x = x + 0.2x = 1.2x = 6x/5.
Let's find an expression for decreasing the product of four and x by five. First, we must find the product of four and x, which can be written as 4x. Then we must decrease this by five, so we must subtract five from 4x, which could be written as 4x - 5.
Now we must set the two expressions equal to one another.
6x/5 = 4x - 5
Subtract 6x/5 from both sides. We can rewrite 4x as 20x/5 so that it has a common denominator with 6x/5.
0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5
0 = 14x/5 - 5
Now we can add five to both sides.
5 = 14x/5
Now we can multiply both sides by 5/14, which is the reciprocal of 14/5.
5(5/14) = (14x/5)(5/14) = x
25/14 = x
The answer is 25/14.

Incorrect

The correct answer is 25/14

Explanation: The problem tells us that increasing x by twenty percent gives us the same thing that we would get if we decreased the product of four and x by five. We need to find expressions for these two situations, and then we can set them equal and solve for x.
Let's find an expression for increasing x by twenty percent. We could represent this as x + 20%x = x + 0.2x = 1.2x = 6x/5.
Let's find an expression for decreasing the product of four and x by five. First, we must find the product of four and x, which can be written as 4x. Then we must decrease this by five, so we must subtract five from 4x, which could be written as 4x - 5.
Now we must set the two expressions equal to one another.
6x/5 = 4x - 5
Subtract 6x/5 from both sides. We can rewrite 4x as 20x/5 so that it has a common denominator with 6x/5.
0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5
0 = 14x/5 - 5
Now we can add five to both sides.
5 = 14x/5
Now we can multiply both sides by 5/14, which is the reciprocal of 14/5.
5(5/14) = (14x/5)(5/14) = x
25/14 = x
The answer is 25/14.
Subtracting 3 from both sides gives us –3x < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.

Correct

Explanation: This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4xs and ks are both equal to v, which means that 4xs and ks must be equal to each other--that is, 4xs = ks. Dividing both sides by s gives 4x = k, which is our solution.

Incorrect

The correct answer is 25/14

Explanation: This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4xs and ks are both equal to v, which means that 4xs and ks must be equal to each other--that is, 4xs = ks. Dividing both sides by s gives 4x = k, which is our solution.

Correct

Explanation:

Incorrect

The correct answer is E

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 9

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 12

Explanation:

Correct

Explanation: To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified

Incorrect

The correct answer is B

Explanation: To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 2.32

Explanation:

Correct

Explanation:

Incorrect

The correct answer is cos x

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 7

Explanation:

Correct

Explanation:

Incorrect

The correct answer is E

Explanation:

Correct

Explanation:

Incorrect

The correct answer is A

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 111 only

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 11

Explanation:

Correct

Explanation:

Incorrect

The correct answer is D

Explanation:

Correct

Explanation:

Incorrect

The correct answer is D

Explanation:

Correct

Explanation:

Incorrect

The correct answer is A

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 1

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is D

Explanation:

Correct

Explanation:

Incorrect

The correct answer is D

Explanation:

Correct

Explanation:

Incorrect

The correct answer is y=3

Explanation:

Correct

Explanation : Simplifying this expression is similar to 1/2 – 1/5. The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2 * 5 = 10. So the problem becomes 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

Incorrect

The correct answer is 3x/10

Explanation : Simplifying this expression is similar to 1/2 – 1/5. The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2 * 5 = 10. So the problem becomes 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

Correct

Explanation : 0/6=0, which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

Incorrect

The correct answer is 0

Explanation : 0/6=0, which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

Correct

Explanation:

Incorrect

The correct answer is 190/96

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 4/11

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation: We start by cross multiplying to get the equation 26t=19t-95. We then subtract 19t from 26t giving us 7t= -95. We then divide by 7, giving us t= (-95)/7.

Incorrect

The correct answer is (-95)/7

Explanation: We start by cross multiplying to get the equation 26t=19t-95. We then subtract 19t from 26t giving us 7t= -95. We then divide by 7, giving us t= (-95)/7.

Correct

Explanation: 1. Solve for x in x/3 = 50
2. x = 150
3.Substitute 150 for x in x/10
4. x = 15

Incorrect

The correct answer is 15

Explanation: 1. Solve for x in x/3 = 50
2. x = 150
3.Substitute 150 for x in x/10
4. x = 15

Correct

Explanation: There are only x * 10 liters of water on the island. n * m equals how many liters are consumed per day. Divide x * 10 liters by n * m. Note the units (days) are correct in the answer.

Incorrect

The correct answer is 10x/mn

Explanation: There are only x * 10 liters of water on the island. n * m equals how many liters are consumed per day. Divide x * 10 liters by n * m. Note the units (days) are correct in the answer.

Correct

Explanation: The amount of money that Lauren can make depends on the number of sweaters that she can make. If she makes at most s sweaters a day, then we can multiply the number of days that she works by s to determine the total number of sweaters she makes.
total number of sweaters = (s)(number of days)
We are told to consider a time interval of three weeks. Because there are seven days in one week, the number of days over this period of time would equal 3(7), or 21 days. In other words, there are 21 days in three weeks Thus, the number of sweaters is equal to the product of s and 21.
total number of sweaters = (s)(21)
Now that we have the number of sweaters Lauren can make, we can multiply this by the cost of each sweater, which is equal to c cents, in order to obtain the amount of money she eared.
amount of money earned = (number of sweaters)(cost of each sweater)
amount of money earned = s(21)(c)
However, because the price of each sweater is given in terms of cents, the amount of money s(21)(c) will be equal to the number of cents she makes. The question, though, asks us to find the amount of money in dollars. We must use a conversion factor to change the number of cents to dollars. Remember that there are 100 cents per dollar

Incorrect

The correct answer is 21sc/100

Explanation: The amount of money that Lauren can make depends on the number of sweaters that she can make. If she makes at most s sweaters a day, then we can multiply the number of days that she works by s to determine the total number of sweaters she makes.
total number of sweaters = (s)(number of days)
We are told to consider a time interval of three weeks. Because there are seven days in one week, the number of days over this period of time would equal 3(7), or 21 days. In other words, there are 21 days in three weeks Thus, the number of sweaters is equal to the product of s and 21.
total number of sweaters = (s)(21)
Now that we have the number of sweaters Lauren can make, we can multiply this by the cost of each sweater, which is equal to c cents, in order to obtain the amount of money she eared.
amount of money earned = (number of sweaters)(cost of each sweater)
amount of money earned = s(21)(c)
However, because the price of each sweater is given in terms of cents, the amount of money s(21)(c) will be equal to the number of cents she makes. The question, though, asks us to find the amount of money in dollars. We must use a conversion factor to change the number of cents to dollars. Remember that there are 100 cents per dollar

Correct

Explanation: To find 40 percent of 30z multiply 30z * 0.4
The result is 12z

Incorrect

The correct answer is 12z

Explanation: To find 40 percent of 30z multiply 30z * 0.4
The result is 12z

Correct

Explanation: The domain means what real number can you plug in that would still make the function work. For this case, we have to worry about the denominator so that it does not equal 0, so we solve the following. 7x – 1 = 0, 7x = 1, x = 1/7, so when x ≠ 1/7 the function will work.

Incorrect

The correct answer is x is not equal to (1/7)

Explanation: The domain means what real number can you plug in that would still make the function work. For this case, we have to worry about the denominator so that it does not equal 0, so we solve the following. 7x – 1 = 0, 7x = 1, x = 1/7, so when x ≠ 1/7 the function will work.

Correct

Explanation: The domain of a function or relation is the set of all possible x-values. Here that is simply a list of the x-coordinates of all of the coordinate pairs. So the domain is {–2, –3, 2, 4}.

Incorrect

The correct answer is {–2, –3, 2, 4}

Explanation: The domain of a function or relation is the set of all possible x-values. Here that is simply a list of the x-coordinates of all of the coordinate pairs. So the domain is {–2, –3, 2, 4}.

Correct

Explanation: Because x and y must be negative integers greater than negative five, then x and y can only be equal to the following values:
x can equal -4, -3, -2, or -1
y can equal -4, -3, -2, or -1
Now we can try all of the combinations of x and y, and see what x # y would equal. It is helpful to note that x # y is the same as y # x because 2yx + y + x = 2xy + x + y. This means that the order of x and y doesn't matter.
-4 # -4 = 2(-4)(-4) + -4 + -4 = 24
-4 # -3 = 2(-4)(-3) + -4 + -3 = 17
-4 # -2 = 10
-4 # -1 = 3
-3 # -3 = 12
-3 # -2 = 7
-3 # -1 = 2
-2 # -2 = 4
-2 # -1 = 1
-1 # -1 = 0
We don't need to find -3 # -4, -2 # -4, etc, because x # y = y # x .
The smallest value of x # y must be 0.

Incorrect

The correct answer is 0

Explanation: Because x and y must be negative integers greater than negative five, then x and y can only be equal to the following values:
x can equal -4, -3, -2, or -1
y can equal -4, -3, -2, or -1
Now we can try all of the combinations of x and y, and see what x # y would equal. It is helpful to note that x # y is the same as y # x because 2yx + y + x = 2xy + x + y. This means that the order of x and y doesn't matter.
-4 # -4 = 2(-4)(-4) + -4 + -4 = 24
-4 # -3 = 2(-4)(-3) + -4 + -3 = 17
-4 # -2 = 10
-4 # -1 = 3
-3 # -3 = 12
-3 # -2 = 7
-3 # -1 = 2
-2 # -2 = 4
-2 # -1 = 1
-1 # -1 = 0
We don't need to find -3 # -4, -2 # -4, etc, because x # y = y # x .
The smallest value of x # y must be 0.

Correct

Explanation: The purpose of this question is to understand when x values will yield y values. The term inside of a square root can be positive or equal to zero in order to yield a value. This means that x can be equal to all real numbers that are -9 or higher, which shows that the domain of the function is all real numbers that are at least -9.

Incorrect

The correct answer is All real numbers greater than or equal to -9

Explanation: The purpose of this question is to understand when x values will yield y values. The term inside of a square root can be positive or equal to zero in order to yield a value. This means that x can be equal to all real numbers that are -9 or higher, which shows that the domain of the function is all real numbers that are at least -9.

Correct

Explanation: The key here is to factor the denominator, bearing in mind that once we do, we can find the values for which the denominator will be 0 and therefore the values for which the function will not be valid.
x3−x=x(x2−1)=x(x+1)(x−1)
We can thus deduce from those three factors that the function will not be valid when x∈{−1,0,1}.

Incorrect

The correct answer is All real numbers except −1, 0 and 1

Explanation: The key here is to factor the denominator, bearing in mind that once we do, we can find the values for which the denominator will be 0 and therefore the values for which the function will not be valid.
x3−x=x(x2−1)=x(x+1)(x−1)
We can thus deduce from those three factors that the function will not be valid when x∈{−1,0,1}.

Correct

Explanation: The domain of a relation is the same as the range of the inverse of the relation. In other words, the x-values of the relation are the y-values of the inverse.

Incorrect

The correct answer is {1, 3, 5, 7}

Explanation: The domain of a relation is the same as the range of the inverse of the relation. In other words, the x-values of the relation are the y-values of the inverse.

Correct

Explanation: We need to be careful here not to confuse the domain and range of a function. The problem specifically concerns the range of the function, which is the set of possible numbers of f(x). It can be helpful to think of the range as all the possible y-values we could have on the points on the graph of f(x).
Notice that dpi{100} f(x) has dpi{100} |4-x| in its equation. Whenever we have an absolute value of some quantity, the result will always be equal to or greater than zero. In other words, |4-x| ≥ ≥ 0. We are asked to find the smallest value in the range of f(x), so let's consider the smallest value of |4-x|, which would have to be zero. Let's see what would happen to f(x) if |4-x|=0.
f(x)=2(0)-2=0-2=-2
This means that when |4-x|=0, f(x)=-2. Let's see what happens when |4-x| gets larger. For example, let's let |4-x|=3.
f(x)=2(3)-2=4
As we can see, as |4-x| gets larger, so does f(x). We want f(x) to be as small as possible, so we are going to want |4-x| to be equal to zero. And, as we already determiend, f(x) equals -2 when |4-x|=0.
The answer is -2.

Incorrect

The correct answer is -2

Explanation: We need to be careful here not to confuse the domain and range of a function. The problem specifically concerns the range of the function, which is the set of possible numbers of f(x). It can be helpful to think of the range as all the possible y-values we could have on the points on the graph of f(x).
Notice that dpi{100} f(x) has dpi{100} |4-x| in its equation. Whenever we have an absolute value of some quantity, the result will always be equal to or greater than zero. In other words, |4-x| ≥ ≥ 0. We are asked to find the smallest value in the range of f(x), so let's consider the smallest value of |4-x|, which would have to be zero. Let's see what would happen to f(x) if |4-x|=0.
f(x)=2(0)-2=0-2=-2
This means that when |4-x|=0, f(x)=-2. Let's see what happens when |4-x| gets larger. For example, let's let |4-x|=3.
f(x)=2(3)-2=4
As we can see, as |4-x| gets larger, so does f(x). We want f(x) to be as small as possible, so we are going to want |4-x| to be equal to zero. And, as we already determiend, f(x) equals -2 when |4-x|=0.
The answer is -2.

Correct

Explanation: {(1, 2), (3, 4), (5, 6), (7, 8)} The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: {2, 4, 6, 8}.
Thus, the domain for the inverse relation will also be {2, 4, 6, 8}.

Incorrect

The correct answer is {2, 4, 6, 8}

Explanation: {(1, 2), (3, 4), (5, 6), (7, 8)} The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
For the original relation, the range is: {2, 4, 6, 8}.
Thus, the domain for the inverse relation will also be {2, 4, 6, 8}.

Correct

Explanation: The range of a function is the set of y-values that a function can take. First let's find the domain. The domain is the set of x-values that the function can take. Here the domain is all real numbers because no x-value will make this function undefined. (Dividing by 0 is an example of an operation that would make the function undefined.) So if any value of x can be plugged into y = x2 + 2, can y take any value also? Not quite! The smallest value that y can ever be is 2. No matter what value of x is plugged in, y = x2 + 2 will never produce a number less than 2. Therefore the range is y ≥ 2.

Incorrect

The correct answer is y ≥ 2

Explanation: The range of a function is the set of y-values that a function can take. First let's find the domain. The domain is the set of x-values that the function can take. Here the domain is all real numbers because no x-value will make this function undefined. (Dividing by 0 is an example of an operation that would make the function undefined.) So if any value of x can be plugged into y = x2 + 2, can y take any value also? Not quite! The smallest value that y can ever be is 2. No matter what value of x is plugged in, y = x2 + 2 will never produce a number less than 2. Therefore the range is y ≥ 2.

Correct

Explanation: Values of x that make the denominator equal zero are not included in the domain. The denominator can be simplified to (x – 3)2, so the value that makes it zero is 3.

Incorrect

The correct answer is 3

Explanation: Values of x that make the denominator equal zero are not included in the domain. The denominator can be simplified to (x – 3)2, so the value that makes it zero is 3.

Correct

Explanation: The function g(x) is equal to 4x + 5, and the notation 2g(x) asks us to multiply the entire function by 2. 2(4x + 5) = 8x + 10. We then subtract 3, the second part of the new equation, to get 8x + 7.

Incorrect

The correct answer is 8x + 7

Explanation: The function g(x) is equal to 4x + 5, and the notation 2g(x) asks us to multiply the entire function by 2. 2(4x + 5) = 8x + 10. We then subtract 3, the second part of the new equation, to get 8x + 7.

Correct

Explanation: 40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).

Incorrect

The correct answer is f(x) = 40 + 0.05(x - 100)

Explanation: 40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).

Correct

Explanation: f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10

Incorrect

The correct answer is 2

Explanation: f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10

Correct

Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.

Incorrect

The correct answer is -2

Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.

Correct

Explanation: The first step is to find what f(10) equals, so f(10)=5(10) – 10 = 40. Then substitute 40 into the second equation: 5(40) – 10 = 200 – 10 = 190.

Incorrect

The correct answer is 190

Explanation: The first step is to find what f(10) equals, so f(10)=5(10) – 10 = 40. Then substitute 40 into the second equation: 5(40) – 10 = 200 – 10 = 190.

Correct

Explanation: The domain means what real number can you plug in that would still make the function work. For this case, we have to worry about the denominator so that it does not equal 0, so we solve the following. 7x – 1 = 0, 7x = 1, x = 1/7, so when x ≠ 1/7 the function will work.

Incorrect

The correct answer is x ≠ (1/7)

Explanation: The domain means what real number can you plug in that would still make the function work. For this case, we have to worry about the denominator so that it does not equal 0, so we solve the following. 7x – 1 = 0, 7x = 1, x = 1/7, so when x ≠ 1/7 the function will work.

Correct

Explanation: The domain of a function or relation is the set of all possible x-values. Here that is simply a list of the x-coordinates of all of the coordinate pairs. So the domain is {–2, –3, 2, 4}.

Incorrect

The correct answer is {–2, –3, 2, 4}

Explanation: The domain of a function or relation is the set of all possible x-values. Here that is simply a list of the x-coordinates of all of the coordinate pairs. So the domain is {–2, –3, 2, 4}.

Correct

Explanation: Because x and y must be negative integers greater than negative five, then x and y can only be equal to the following values:
x can equal -4, -3, -2, or -1
y can equal -4, -3, -2, or -1
Now we can try all of the combinations of x and y, and see what x # y would equal. It is helpful to note that x # y is the same as y # x because 2yx + y + x = 2xy + x + y. This means that the order of x and y doesn't matter.
-4 # -4 = 2(-4)(-4) + -4 + -4 = 24
-4 # -3 = 2(-4)(-3) + -4 + -3 = 17
-4 # -2 = 10
-4 # -1 = 3
-3 # -3 = 12
-3 # -2 = 7
-3 # -1 = 2
-2 # -2 = 4
-2 # -1 = 1
-1 # -1 = 0
We don't need to find -3 # -4, -2 # -4, etc, because x # y = y # x .
The smallest value of x # y must be 0.

Incorrect

The correct answer is 0

Explanation: Because x and y must be negative integers greater than negative five, then x and y can only be equal to the following values:
x can equal -4, -3, -2, or -1
y can equal -4, -3, -2, or -1
Now we can try all of the combinations of x and y, and see what x # y would equal. It is helpful to note that x # y is the same as y # x because 2yx + y + x = 2xy + x + y. This means that the order of x and y doesn't matter.
-4 # -4 = 2(-4)(-4) + -4 + -4 = 24
-4 # -3 = 2(-4)(-3) + -4 + -3 = 17
-4 # -2 = 10
-4 # -1 = 3
-3 # -3 = 12
-3 # -2 = 7
-3 # -1 = 2
-2 # -2 = 4
-2 # -1 = 1
-1 # -1 = 0
We don't need to find -3 # -4, -2 # -4, etc, because x # y = y # x .
The smallest value of x # y must be 0.

Correct

Explanation:

Incorrect

The correct answer is [0,∞)

Explanation:

Correct

Explanation:

Incorrect

The correct answer is x∈[5,10]

Explanation:

Correct

Explanation:

Incorrect

The correct answer is x = -4, x = 2

Explanation:

Correct

Explanation:

Incorrect

The correct answer is E

Explanation:

Correct

Explanation:

Incorrect

The correct answer is 3

Explanation:

Correct

Explanation: If the equation
C=1.2+.5h
were graphed, the result would be a line with a slope of 0.5 and a y-intercept of 1.2. 0.5 represents the amount Tonya pays per hour to work at a computer, because we know that the rate is $0.50, and C represents the total amount she pays. Because we must add 1.2 (or $1.20) to the total amount of hours multiplied by the hourly rate in order to get the total amount Tonya paid, we can assume there is another charge for renting a computer, in addition to the hourly rate, and that that charge is $1.20. Therefore, the y-intercept of the graph of the equation represents the initial cost of using a computer.

Incorrect

The initial cost of using a computer.

Explanation: If the equation
C=1.2+.5h
were graphed, the result would be a line with a slope of 0.5 and a y-intercept of 1.2. 0.5 represents the amount Tonya pays per hour to work at a computer, because we know that the rate is $0.50, and C represents the total amount she pays. Because we must add 1.2 (or $1.20) to the total amount of hours multiplied by the hourly rate in order to get the total amount Tonya paid, we can assume there is another charge for renting a computer, in addition to the hourly rate, and that that charge is $1.20. Therefore, the y-intercept of the graph of the equation represents the initial cost of using a computer.

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is D

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is E

Explanation:

Correct

Explanation:

Incorrect

The correct answer is D

Explanation:

Correct

Explanation:

Incorrect

The correct answer is A

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is A

Explanation:

Correct

Explanation:

Incorrect

The correct answer is A

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is B

Explanation:

Correct

Explanation:

Incorrect

The correct answer is B

Explanation:

Correct

Explanation:

Incorrect

The correct answer is B

Explanation:

Correct

Explanation:

Incorrect

The correct answer is B

Explanation:

Correct

Explanation:

Incorrect

The correct answer is A

Explanation:

Correct

Explanation : Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.

Incorrect

The correct answer is 2/7

Explanation : Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.

Correct

Explanation : Start by combining like terms.
4x + 5 = 13x + 4 – x – 9
4x + 5 = 12x – 5
–8x = –10
x = 5/4

Incorrect

The correct answer is 5/4

Explanation : Start by combining like terms.
4x + 5 = 13x + 4 – x – 9
4x + 5 = 12x – 5
–8x = –10
x = 5/4

Correct

Explanation : First we solve for x.
Subtracting 3 from both sides gives us –3x < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.

Incorrect

The correct answer is -6

Explanation : First we solve for x.
Subtracting 3 from both sides gives us –3x < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.

Correct

Explanation : The problem tells us that increasing x by twenty percent gives us the same thing that we would get if we decreased the product of four and x by five. We need to find expressions for these two situations, and then we can set them equal and solve for x.
Let's find an expression for increasing x by twenty percent. We could represent this as x + 20%x = x + 0.2x = 1.2x = 6x/5.
Let's find an expression for decreasing the product of four and x by five. First, we must find the product of four and x, which can be written as 4x. Then we must decrease this by five, so we must subtract five from 4x, which could be written as 4x - 5.
Now we must set the two expressions equal to one another.
6x/5 = 4x - 5
Subtract 6x/5 from both sides. We can rewrite 4x as 20x/5 so that it has a common denominator with 6x/5.
0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5
0 = 14x/5 - 5
Now we can add five to both sides.
5 = 14x/5
Now we can multiply both sides by 5/14, which is the reciprocal of 14/5.
5(5/14) = (14x/5)(5/14) = x
25/14 = x

Incorrect

The correct answer is 25/14

Explanation : The problem tells us that increasing x by twenty percent gives us the same thing that we would get if we decreased the product of four and x by five. We need to find expressions for these two situations, and then we can set them equal and solve for x.
Let's find an expression for increasing x by twenty percent. We could represent this as x + 20%x = x + 0.2x = 1.2x = 6x/5.
Let's find an expression for decreasing the product of four and x by five. First, we must find the product of four and x, which can be written as 4x. Then we must decrease this by five, so we must subtract five from 4x, which could be written as 4x - 5.
Now we must set the two expressions equal to one another.
6x/5 = 4x - 5
Subtract 6x/5 from both sides. We can rewrite 4x as 20x/5 so that it has a common denominator with 6x/5.
0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5
0 = 14x/5 - 5
Now we can add five to both sides.
5 = 14x/5
Now we can multiply both sides by 5/14, which is the reciprocal of 14/5.
5(5/14) = (14x/5)(5/14) = x
25/14 = x

Correct

Explanation : This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4xs and ks are both equal to v, which means that 4xs and ks must be equal to each other--that is, 4xs = ks. Dividing both sides by s gives 4x = k, which is our solution.

Incorrect

The correct answer is 4x

Explanation : This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4xs and ks are both equal to v, which means that 4xs and ks must be equal to each other--that is, 4xs = ks. Dividing both sides by s gives 4x = k, which is our solution.

Correct

Explanation:

Incorrect

The correct answer is E

Explanation:

Correct

Explanation:

Incorrect

The correct answer is -9

Explanation:

Correct

Explanation:

Incorrect

The correct answer is x=−1

Explanation:

Correct

Explanation:

Incorrect

The correct answer is a=12 a=−5

Explanation:

Correct

Explanation:

Incorrect

The correct answer is E

Explanation:

Correct

Explanation:

Incorrect

The correct answer is A

Explanation:

Correct

Explanation:

Incorrect

The correct answer is D

Explanation:

Correct

Explanation:

Incorrect

The correct answer is B

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation:

Incorrect

The correct answer is C

Explanation:

Correct

Explanation: m+2<0 and m+5>0, so m<−2 and m>−5. The only integers between −2 and −5 are −3 and −4.

Incorrect

The correct answer is -3.

Explanation: m+2<0 and m+5>0, so m<−2 and m>−5. The only integers between −2 and −5 are −3 and −4.

Correct

Explanation: The median weight of a box of cereal is 360 grams. This should be an allowable value of w. Substituting 360 for w into each answer choice, the only true results are:
|w−360|≤4
|360−360|≤4
0≤4
and:
|w+360|≥4
|360+360|≥4
720≥4
Notice that any positive value for w satisfies the second inequality above. Since w must be between 356 and 364, the first inequality above is the only reasonable choice.

Incorrect

The correct answer is |w−360| is less than and equal to 4

Explanation: The median weight of a box of cereal is 360 grams. This should be an allowable value of w. Substituting 360 for w into each answer choice, the only true results are:
|w−360|≤4
|360−360|≤4
0≤4
and:
|w+360|≥4
|360+360|≥4
720≥4
Notice that any positive value for w satisfies the second inequality above. Since w must be between 356 and 364, the first inequality above is the only reasonable choice.

Correct

Explanation: Absolute value problems always have two sides: one positive and one negative.
First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.
Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).
We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.

Incorrect

The correct answer is z ≤ −2 or z ≥ 8

Explanation: Absolute value problems always have two sides: one positive and one negative.
First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.
Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).
We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.

Correct

Explanation: To solve this problem, add the two equations together:
x + 1 < 4
y − 2 < −1
x + 1 + y − 2 < 4 − 1
x + y − 1 < 3
x + y < 4
The only answer choice that satisfies this equation is 0, because 0 is less than 4.

Incorrect

The correct answer is 0

Explanation: To solve this problem, add the two equations together:
x + 1 < 4
y − 2 < −1
x + 1 + y − 2 < 4 − 1
x + y − 1 < 3
x + y < 4
The only answer choice that satisfies this equation is 0, because 0 is less than 4.

Correct

Explanation: The equation simplifies to x > -1.41. -1 is the answer.

Incorrect

The correct answer is -1

Explanation: The equation simplifies to x > -1.41. -1 is the answer.

Correct

Explanation: Absolute value problems always have two sides: one positive and one negative.
First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.
Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).
We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.

Incorrect

The correct answer is z ≤ −2 or z ≥ 8

Explanation: Absolute value problems always have two sides: one positive and one negative.
First, take the problem as is and drop the absolute value signs for the positive side: z – 3 ≥ 5. When the original inequality is multiplied by –1 we get z – 3 ≤ –5.
Solve each inequality separately to get z ≤ –2 or z ≥ 8 (the inequality sign flips when multiplying or dividing by a negative number).
We can verify the solution by substituting in 0 for z to see if we get a true or false statement. Since –3 ≥ 5 is always false we know we want the two outside inequalities, rather than their intersection.

Correct

Explanation: We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.
|x+7|≤3x+13 We need to set-up two equations since it's absolute value.
x+7≤3x+13 Subtract x,7 on both sides.
−6≤2x Divide 2 on both sides.
−3≤x
−(x+7)≤3x+13 Distribute the negative sign to each term in the parenthesis.
−x−7≤3x+13 Add x and subtract 13 on both sides.
−20≤4x Divide 4 on both sides.
−5≤x We must check each answer. Let's try 0.
|0+7|<3(0)+13 7<13 This is true therefore −3≤x is a correct answer. Let's next try −4.
|−4+7|<3(−4)+13 3<1 This is not true therefore −5≤x is not correct.
Final answer is just −3≤x.

Incorrect

The correct answer is −3 ≤ x

Explanation: We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.
|x+7|≤3x+13 We need to set-up two equations since it's absolute value.
x+7≤3x+13 Subtract x,7 on both sides.
−6≤2x Divide 2 on both sides.
−3≤x
−(x+7)≤3x+13 Distribute the negative sign to each term in the parenthesis.
−x−7≤3x+13 Add x and subtract 13 on both sides.
−20≤4x Divide 4 on both sides.
−5≤x We must check each answer. Let's try 0.
|0+7|<3(0)+13 7<13 This is true therefore −3≤x is a correct answer. Let's next try −4.
|−4+7|<3(−4)+13 3<1 This is not true therefore −5≤x is not correct.
Final answer is just −3≤x.

Correct

Explanation: To solve this problem, add the two equations together:
x+1<4
y−2<−1
x+1+y−2<4−1
x+y−1<3
x+y<4
The only answer choice that satisfies this equation is 0, because 0 is less than 4.

Incorrect

The correct answer is 0

Explanation: To solve this problem, add the two equations together:
x+1<4
y−2<−1
x+1+y−2<4−1
x+y−1<3
x+y<4
The only answer choice that satisfies this equation is 0, because 0 is less than 4.

Correct

Explanation: To solve 3x+2≤49, isolate x.
3x≤47
Divide by three on both sides. x≤47/3

Incorrect

The correct answer is x ≤ 47/3

Explanation: To solve 3x+2≤49, isolate x.
3x≤47
Divide by three on both sides. x≤47/3

Correct

Explanation: First, solve the inequality 5x−9≥6:
5x−9≥6
5x≥15
x≥3
Since we are dealing with absolute value, 5x−9≤−6 must also be true; therefore:
5x−9≤−6
5x≤3
x≤3/5

Incorrect

The correct answer is x ≥ 3 , x ≤ 3/5

Explanation: First, solve the inequality 5x−9≥6:
5x−9≥6
5x≥15
x≥3
Since we are dealing with absolute value, 5x−9≤−6 must also be true; therefore:
5x−9≤−6
5x≤3
x≤3/5

Correct

Explanation: xy(5x + 5y)/z

Incorrect

The correct answer is 5x² + y²/z

Explanation: xy(5x + 5y)/z

Correct

Explanation: First, we need to find all of the values that are in the set S, and then we need to find the values in T. Once we do this, we must find the numbers in the intersection of S and T, which means we must find the values contained in BOTH sets S and T.
S contains all of the values of x such that 2x + 4 < 8. We need to solve this inequality.
2x + 4 < 8
Subtract 4 from both sides.
2x < 4
Divide by 2.
x < 2
Thus, S contains all of the values of x that are less than (but not equal to) 2.
Now, we need to do the same thing to find the values contained in T.
-2x + 3 < 8
Subtract 3 from both sides.
-2x < 5
Divide both sides by -2. Remember, when multiplying or dividing an inequality by a negative number, we must switch the sign.
x > -5/2
Therefore, T contains all of the values of x that are greater than -5/2, or -2.5.
Next, we must find the values that are contained in both S and T. In order to be in both sets, these numbers must be less than 2, but also greater than -2.5. Thus, the intersection of S and T consists of all numbers between -2.5 and 2.
The question asks us to find the sum of the integers in the intersection of S and T. This means we must find all of the integers between -2.5 and 2.
The integers between -2.5 and 2 are the following: -2, -1, 0, and 1. We cannot include 2, because the values in S are LESS than but not equal to 2.
Lastly, we add up the values -2, -1, 0, and 1. The sum of these is -2.
The answer is -2.

Incorrect

The correct answer is -2

Explanation: First, we need to find all of the values that are in the set S, and then we need to find the values in T. Once we do this, we must find the numbers in the intersection of S and T, which means we must find the values contained in BOTH sets S and T.
S contains all of the values of x such that 2x + 4 < 8. We need to solve this inequality.
2x + 4 < 8
Subtract 4 from both sides.
2x < 4
Divide by 2.
x < 2
Thus, S contains all of the values of x that are less than (but not equal to) 2.
Now, we need to do the same thing to find the values contained in T.
-2x + 3 < 8
Subtract 3 from both sides.
-2x < 5
Divide both sides by -2. Remember, when multiplying or dividing an inequality by a negative number, we must switch the sign.
x > -5/2
Therefore, T contains all of the values of x that are greater than -5/2, or -2.5.
Next, we must find the values that are contained in both S and T. In order to be in both sets, these numbers must be less than 2, but also greater than -2.5. Thus, the intersection of S and T consists of all numbers between -2.5 and 2.
The question asks us to find the sum of the integers in the intersection of S and T. This means we must find all of the integers between -2.5 and 2.
The integers between -2.5 and 2 are the following: -2, -1, 0, and 1. We cannot include 2, because the values in S are LESS than but not equal to 2.
Lastly, we add up the values -2, -1, 0, and 1. The sum of these is -2.
The answer is -2.

Correct

Explanation: In an absolute value inequality, the absolute value expression must be isolated first, as follows:
−12−|−4y+52|>32
Adding 12 to both sides:
−12−|−4y+52|+12>32+12
−|−4y+52|>44
Multiplying both sides by −1, and switching the inequality symbol due to multiplication by a negative number:
−|−4y+52|⋅(−1)<44⋅(−1)
|−4y+52|<−44
We do not need to go further. An absolute value expression must always be greater than or equal to 0; it is impossible for the expression |−4y+52| to be less than any negative number. The inequality has no solution.

Incorrect

The correct answer is The inequality has no solution.

Explanation: In an absolute value inequality, the absolute value expression must be isolated first, as follows:
−12−|−4y+52|>32
Adding 12 to both sides:
−12−|−4y+52|+12>32+12
−|−4y+52|>44
Multiplying both sides by −1, and switching the inequality symbol due to multiplication by a negative number:
−|−4y+52|⋅(−1)<44⋅(−1)
|−4y+52|<−44
We do not need to go further. An absolute value expression must always be greater than or equal to 0; it is impossible for the expression |−4y+52| to be less than any negative number. The inequality has no solution.

Correct

Explanation: The inequality that is presented in the problem is:
8−7x≤11x+4
Start by moving your variables to one side of the inequality and all other numbers to the other side:
−7x−11x≤4−8
−18x≤−4
Divide both sides of the equation by −18. Remember to flip the direction of the inequality's sign since you are dividing by a negative number!
x≥−4/−18
Reduce:
x≥2/9
The only answer choice with a value greater than 2/9 is 4/9.

Incorrect

The correct answer is 4/9

Explanation: The inequality that is presented in the problem is:
8−7x≤11x+4
Start by moving your variables to one side of the inequality and all other numbers to the other side:
−7x−11x≤4−8
−18x≤−4
Divide both sides of the equation by −18. Remember to flip the direction of the inequality's sign since you are dividing by a negative number!
x≥−4/−18
Reduce:
x≥2/9
The only answer choice with a value greater than 2/9 is 4/9.

Correct

Explanation: The equation simplifies to x > -1.41. -1 is the answer.

Incorrect

The correct answer is -1

Explanation: The equation simplifies to x > -1.41. -1 is the answer.

Correct

Explanation: 3x+7≥−2x+4
3x≥−2x−3
5x≥−3
x≥−3/5

Incorrect

The correct answer is x ≥ −3/5

Explanation: 3x+7≥−2x+4
3x≥−2x−3
5x≥−3
x≥−3/5

Correct

Explanation: k is such that:
3/k−5/7>0
Add 5/7 to each side of the inequality:
3/k>5/7
Multiply each side of the inequality by 3:
21/k>5
Multiply each side of the inequality by k:
21>5k
Divide each side of the inequality by 5:
k<21/5
You can now change the fraction on the right side of the inequality to decimal form.
k<21/5=20/5+1/5=4.2
The correct answer is 4, since k has to be less than 4.2 for the expression to be greater than zero.

Incorrect

The correct answer is 4

Explanation: k is such that:
3/k−5/7>0
Add 5/7 to each side of the inequality:
3/k>5/7
Multiply each side of the inequality by 3:
21/k>5
Multiply each side of the inequality by k:
21>5k
Divide each side of the inequality by 5:
k<21/5
You can now change the fraction on the right side of the inequality to decimal form.
k<21/5=20/5+1/5=4.2
The correct answer is 4, since k has to be less than 4.2 for the expression to be greater than zero.

Correct

Explanation: The absolute value inequality
|−4x+17|≥67
can be rewritten as the compound inequality
−4x+17≤−67 or −4x+17≥67
Solve each inequality separately, using the properties of inequality to isolate the variable on the left side:
−4x+17≤−67
Subtract 17 from both sides:
−4x+17−17≤−67−17
−4x≤−84
Divide both sides by −4, switching the inequality symbol since you are dividing by a negative number:
−4x÷(−4)≥−84÷(−4)
x≥21,
which in interval notation is [21,∞)
The same steps are performed with the other inequality:
−4x+17≥67
−4x+17−17≥67−17
−4x≥50
−4x÷(−4)≤50÷(−4)
x≤−12.5
which in interval notation is (−∞,−12.5].
The correct response is the union of these two sets, which is
(−∞,−12.5]∪[21,∞).

Incorrect

The correct answer is (−∞,−12.5] ∪ [21,∞)

Explanation: The absolute value inequality
|−4x+17|≥67
can be rewritten as the compound inequality
−4x+17≤−67 or −4x+17≥67
Solve each inequality separately, using the properties of inequality to isolate the variable on the left side:
−4x+17≤−67
Subtract 17 from both sides:
−4x+17−17≤−67−17
−4x≤−84
Divide both sides by −4, switching the inequality symbol since you are dividing by a negative number:
−4x÷(−4)≥−84÷(−4)
x≥21,
which in interval notation is [21,∞)
The same steps are performed with the other inequality:
−4x+17≥67
−4x+17−17≥67−17
−4x≥50
−4x÷(−4)≤50÷(−4)
x≤−12.5
which in interval notation is (−∞,−12.5].
The correct response is the union of these two sets, which is
(−∞,−12.5]∪[21,∞).

Correct

Explanation: First step is to rewrite 4x+5≥y+3
4x+5≥y+3
4x+2≥y
Next step is to find the vertices of the bounded region. We do this by plugging in the x bounds into the y equation. Don't forgot to set up the other x and y bounds, which are given pretty much.
The vertices are
(1,2)
(5,2)
(1,7)
(5,22)
Now we plug each coordinate into f(x,y), and what the maximum value is.
(1,2)=3(1)+3(2)=9
(5,2)=3(5)+3(1)=21
(1,7)=3(1)+3(7)=25
(5,22)=3(5)+3(22)=81
So the maximum value is 81./p>

Incorrect

The correct answer is 81

Explanation: First step is to rewrite 4x+5≥y+3
4x+5≥y+3
4x+2≥y
Next step is to find the vertices of the bounded region. We do this by plugging in the x bounds into the y equation. Don't forgot to set up the other x and y bounds, which are given pretty much.
The vertices are
(1,2)
(5,2)
(1,7)
(5,22)
Now we plug each coordinate into f(x,y), and what the maximum value is.
(1,2)=3(1)+3(2)=9
(5,2)=3(5)+3(1)=21
(1,7)=3(1)+3(7)=25
(5,22)=3(5)+3(22)=81
So the maximum value is 81.

Correct

Explanation: This inequality could be rewritten as:
4x + 14 > 30 OR 4x + 14 < –30
Solve each for x:
4x + 14 > 30; 4x > 16; x > 4
4x + 14 < –30; 4x < –44; x < –11
Therefore, anything between –11 and 4 (inclusive) will not work. Hence, the answer is 7.

Incorrect

The correct answer is 7

Explanation: This inequality could be rewritten as:
4x + 14 > 30 OR 4x + 14 < –30
Solve each for x:
4x + 14 > 30; 4x > 16; x > 4
4x + 14 < –30; 4x < –44; x < –11
Therefore, anything between –11 and 4 (inclusive) will not work. Hence, the answer is 7.

Correct

Explanation: For this problem, we must take into account the absolute value.
First, we solve for 2x – 2 > 20. But we must also solve for 2x – 2 < –20 (please notice that we negate 20 and we also flip the inequality sign).
First step:
2x – 2 > 20
2x > 22
x > 11
Second step:
2x – 2 < –20
2x < –18
x < –9
Therefore, x > 11 and x < –9.
A possible value for x would be –10 since that is less than –9.
Note: the value 11 would not be a possible value for x because the inequality sign given does not include an equal sign.

Incorrect

The correct answer is -10

Explanation: For this problem, we must take into account the absolute value.
First, we solve for 2x – 2 > 20. But we must also solve for 2x – 2 < –20 (please notice that we negate 20 and we also flip the inequality sign).
First step:
2x – 2 > 20
2x > 22
x > 11
Second step:
2x – 2 < –20
2x < –18
x < –9
Therefore, x > 11 and x < –9.
A possible value for x would be –10 since that is less than –9.
Note: the value 11 would not be a possible value for x because the inequality sign given does not include an equal sign.

Correct

Explanation: m+2<0 and m+5>0, so m<−2 and m>−5. The only integers between −2 and −5 are −3 and −4.

Incorrect

The correct answer is -3

Explanation: m+2<0 and m+5>0, so m<−2 and m>−5. The only integers between −2 and −5 are −3 and −4.

Correct

Explanation: If each pencil sells at 50 cents, x pencils will sell at 50x. The smallest value of x such that:
50x is greater than equal to 1200+20x
x is greater than and equal to 40

Incorrect

The correct answer is 40

Explanation: If each pencil sells at 50 cents, x pencils will sell at 50x. The smallest value of x such that:
50x ≥ 1200+20x
x ≥ 40

Correct

Explanation: We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.
|6x−45|≤75 We need to set-up two equations since its absolute value.
6x−45≤75 Add 45 on both sides.
6x≤120 Divide 6 on both sides.
x≤20
−(6x−45)≤75 Divide −1 on both sides which flips the sign.
6x−45≥−75 Add 45 on both sides.
6x≥−30 Divide 6 on both sides.
x≥−5
Since we have the x's being either greater than or less than the values, we can combine them to get −5≤x≤20.

Incorrect

The correct answer is −5 ≤ x ≤ 20

Explanation: We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.
|6x−45|≤75 We need to set-up two equations since its absolute value.
6x−45≤75 Add 45 on both sides.
6x≤120 Divide 6 on both sides.
x≤20
−(6x−45)≤75 Divide −1 on both sides which flips the sign.
6x−45≥−75 Add 45 on both sides.
6x≥−30 Divide 6 on both sides.
x≥−5
Since we have the x's being either greater than or less than the values, we can combine them to get −5≤x≤20.

Correct

Explanation: Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.

Incorrect

The correct answer is 2/7

Explanation: Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.

Correct

Explanation: Start by combining like terms.
4x + 5 = 13x + 4 – x – 9
4x + 5 = 12x – 5
–8x = –10
x = 5/4

Incorrect

The correct answer is 5/4

Explanation: Start by combining like terms.
4x + 5 = 13x + 4 – x – 9
4x + 5 = 12x – 5
–8x = –10
x = 5/4

Correct

Explanation: First we solve for x.
Subtracting 3 from both sides gives us –3x < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.

Incorrect

The correct answer is -6

Explanation: First we solve for x.
Subtracting 3 from both sides gives us –3x < 17.
Dividing by –3 gives us x > –17/3.
–6 is less than –17/3.

Correct

Explanation: The problem tells us that increasing x by twenty percent gives us the same thing that we would get if we decreased the product of four and x by five. We need to find expressions for these two situations, and then we can set them equal and solve for x.
Let's find an expression for increasing x by twenty percent. We could represent this as x + 20%x = x + 0.2x = 1.2x = 6x/5.
Let's find an expression for decreasing the product of four and x by five. First, we must find the product of four and x, which can be written as 4x. Then we must decrease this by five, so we must subtract five from 4x, which could be written as 4x - 5.
Now we must set the two expressions equal to one another.
6x/5 = 4x - 5
Subtract 6x/5 from both sides. We can rewrite 4x as 20x/5 so that it has a common denominator with 6x/5.
0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5
0 = 14x/5 - 5
Now we can add five to both sides.
5 = 14x/5
Now we can multiply both sides by 5/14, which is the reciprocal of 14/5.
5(5/14) = (14x/5)(5/14) = x
25/14 = x
The answer is 25/14.

Incorrect

The correct answer is 25/14

Explanation: The problem tells us that increasing x by twenty percent gives us the same thing that we would get if we decreased the product of four and x by five. We need to find expressions for these two situations, and then we can set them equal and solve for x.
Let's find an expression for increasing x by twenty percent. We could represent this as x + 20%x = x + 0.2x = 1.2x = 6x/5.
Let's find an expression for decreasing the product of four and x by five. First, we must find the product of four and x, which can be written as 4x. Then we must decrease this by five, so we must subtract five from 4x, which could be written as 4x - 5.
Now we must set the two expressions equal to one another.
6x/5 = 4x - 5
Subtract 6x/5 from both sides. We can rewrite 4x as 20x/5 so that it has a common denominator with 6x/5.
0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5
0 = 14x/5 - 5
Now we can add five to both sides.
5 = 14x/5
Now we can multiply both sides by 5/14, which is the reciprocal of 14/5.
5(5/14) = (14x/5)(5/14) = x
25/14 = x
The answer is 25/14.

Correct

Explanation: This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4xs and ks are both equal to v, which means that 4xs and ks must be equal to each other--that is, 4xs = ks. Dividing both sides by s gives 4x = k, which is our solution.

Incorrect

The correct answer is 4x

Explanation: This question gives two equalities and one inequality. The inequality (sv ≠ 0) simply says that neither s nor v is 0. The two equalities tell us that 4xs and ks are both equal to v, which means that 4xs and ks must be equal to each other--that is, 4xs = ks. Dividing both sides by s gives 4x = k, which is our solution.