AnswersGrade 7 MathematicsInequalities

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1
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Jenna created the given graph to represent the solution to the inequality negative 6 is less than x Expand Image What error did she make?

A
She should have used an open circle at the end of the ray.
B
She should have pointed the arrow to the left.
C
She should have ended the ray with a circle at negative 7 .
D
She should have ended the ray with a circle at negative 5 .
2
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Mercedes receives a 25 dollars gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs 1 point 2 9 dollars Write and solve an inequality to determine m , the number of songs Mercedes can purchase. What is the approximate solution to the inequality? Round to the nearest whole number.

A
m is greater than or equal to 32
B
m is less than or equal to 19
C
m is less than or equal to 32
D
m is greater than or equal to 19
3

Ellen drew a graph showing the solution to an inequality. Expand Image Which inequality does Ellen’s graph show the solution to?

A
3 point 2 5 is greater than 2 point 5 plus r
B
negative 3 point 2 5 is greater than negative 2 point 5 plus r
C
negative 3 point 2 5 is less than negative 2 point 5 plus r
D
3 point 2 5 is less than 2 point 5 plus r
4

Which inequality represents the sentence given? The difference of negative 3 point 2 and the sum of a number and 19 point 1 is at most 14 point 2

A
negative 3 point 2 minus x plus 19 point 1 is greater than or equal to 14 point 2
B
negative 3 point 2 minus open paren x plus 19 point 1 close paren is less than or equal to 14 point 2
C
negative 3 point 2 minus open paren x plus 19 point 1 close paren is greater than or equal to 14 point 2
D
negative 3 point 2 minus x plus 19 point 1 is less than or equal to 14 point 2
5

Allen is running a marathon. He would like to finish the race in under 5 point 5 hours. He has already run 3 hours. The inequality 3 plus t is less than 5 point 5 represents the situation. Which number line shows how much longer Allen can run and still meet his goal?

A
Image with description A number line ranges from 0 to 3 by one halves. The number line represents the variable t. An open circle is on 2 point 5. A ray is drawn from that circle pointing to the left.
B
Image with description A number line ranges from 0 to 3 by one halves. The number line represents the variable t. An open circle is on 2 point 5. A ray is drawn from that circle pointing to the right.
C
Image with description A number line ranges from 0 to 3 by one halves. The number line represents the variable t. A closed circle is on 2 point 5. A ray is drawn from that circle pointing to the left.
D
Image with description A number line ranges from 0 to 3 by one halves. The number line represents the variable t. A closed circle is on 2 point 5. A ray is drawn from that circle pointing to the right.
6

Rico represents the inequality negative 3 times open paren the fraction with numerator 8 and denominator x minus 5 close paren is greater than negative 16 with the sentence “The product of negative 3 and the quotient of 8 and the difference of a number and 5 is at least negative 16 ” Which describes Rico’s error?

A
The expression is translated incorrectly. The numerator and the denominator of the division expression should be reversed.
B
The inequality symbol is translated incorrectly. The words “at least” should be represented as less than or equal to instead of greater than.
C
The expression is translated incorrectly. The order of the terms in the subtraction expression should be reversed.
D
The inequality symbol is translated incorrectly. The words “at least” should be represented as greater than or equal to instead of greater than.
7

Which graph represents the solution set of the inequality −9>x ?

A
Image with description A number line ranges from negative 13 to negative 7 by ones. A closed circle is on negative 9. A ray is drawn from that circle pointing to the left.
B
Image with description A number line ranges from negative 13 to negative 7 by ones. An open circle is on negative 9. A ray is drawn from that circle pointing to the left.
C
Image with description A number line ranges from negative 13 to negative 7 by ones. A closed circle is on negative 9. A ray is drawn from that circle pointing to the right.
D
Image with description A number line ranges from negative 13 to negative 7 by ones. An open circle is on negative 9. A ray is drawn from that circle pointing to the right.
8

Kelly’s first four test grades of the period were 80 , 72 , 96 , and 88 Which inequality represents the grades she can earn on the fifth test to have a test average of no less than 80 ?

A
g is greater than or equal to 16
B
g is less than or equal to 64
C
g is greater than or equal to 64
D
g is less than or equal to 16
9

Michael is on page 28 of a 315 -page book. He must finish the book within the next 14 days. He solved the inequality 28 plus 14 p is less than or equal to 315 to find the minimum number of pages he must read per day to finish the book on time. What error did Michael make when he wrote this inequality to model the situation?

A
He did not recognize that 315 is not a multiple of 14 and should have solved 28 plus 14 p is less than 315 .
B
He did not use the correct value as the coefficient of p and should have solved 14 plus 28 p is less than or equal to 315 .
C
He did not make the variable the minimum number of pages and should have solved 28 plus 14 p is greater than or equal to 315 .
D
He did not account correctly for the 28 pages already read and should have solved 14 p is less than or equal to 315 plus 28 .
10

Solve the following inequality. 6.3⁢r<−45.36 Which graph shows the correct solution?

A
Image with description A number line ranges from negative 77 to negative 67 by ones. An open circle is on negative 72. A ray is drawn from that circle pointing to the left.
B
Image with description A number line ranges from negative 7 point 7 to negative 6 point 8 by one tenths. An open circle is on negative 7 point 2. A ray is drawn from that circle pointing to the right.
C
Image with description A number line ranges from negative 77 to negative 67 by ones. An open circle is on negative 72. A ray is drawn from that circle pointing right.
D
Image with description A number line ranges from negative 7 point 7 to negative 6 point 8 by one tenths. An open circle is on negative 7 point 2. A ray is drawn from that circle pointing to the left.
11

What is the best first step in solving negative 4 x plus 2 fifths is greater than 5 tenths ?

A
Subtract 2 fifths from both sides.
B
Divide both sides by 10 and reverse the inequality symbol.
C
Multiply both sides by negative 4 and reverse the inequality symbol.
D
Add 2 fifths to both sides.
12

According to the properties of inequality, when should the inequality symbol be reversed when solving a two-step inequality in the given form? A x plus b is greater than c

A
when b is positive
B
when A is negative
C
when A is positive
D
when b is negative

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