AnswersGrade 7 MathematicsSolving Two-Step Inequalities

Solving Two-Step Inequalities — Quiz Answers

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1
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Which graph shows the solution set for 2 x plus 3 is greater than negative 9 ?

A
Image with description A number line ranges from negative 8 to 2 by ones. An open circle is on negative 6. A ray is drawn from that circle pointing to the right.
B
Image with description A number line ranges from negative 8 to 2 by ones. An open circle is on negative 6. A ray is drawn from that circle pointing to the left.
C
Image with description A number line ranges from negative 8 to 2 by ones. An open circle is on negative 3. A ray is drawn from that circle pointing to the left.
D
Image with description A number line ranges from negative 8 to 2 by ones. An open circle is on negative 3. A ray is drawn from that circle pointing to the right.
2
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Deepak is a landscaper who charges 30 dollars for each job he does plus an additional 15 dollars for each hour he works. He only accepts jobs if he will earn at least 90 dollars per job. He writes this inequality to determine x , the number of hours he must work during each job in order to accomplish this. 30 plus 15 x is greater than or equal to 90 Which best describes the restrictions on the jobs Deepak will accept?

A
He only accepts jobs that last 4 or more hours.
B
He only accepts jobs that last 5 or more hours.
C
He only accepts jobs that last 8 or more hours.
D
He only accepts jobs that last 9 or more hours.
3

What is the solution to 3 x plus 2 point 4 is greater than or equal to 3 point 0 ?

A
x is greater than or equal to 1 point 8
B
x is greater than or equal to 2 point 5
C
x is greater than or equal to 0 point 6
D
x is greater than or equal to 0 point 2
4

For each babysitting job, Tamar charges 6 dollars for bus fare plus 8 dollars per hour. She only accepts babysitting jobs if the total charge is at least 30 dollars What is the minimum number of hours for a babysitting job she would accept?

A
3 hours
B
4 and 1 half hours
C
2 and 1 half hours
D
4 hours
5

Leon needs to save more than 350 dollars to buy a new bike. He has 130 dollars saved so far, and he plans to save 20 dollars each week until he has enough. The given inequality represents x , the number of weeks he must save to have the extra money needed. 130 plus 20 x is greater than 350 Which best describes the number of weeks he must save before he can buy his bike?

A
He must save for 11 or more weeks.
B
He must save for 24 or more weeks.
C
He must save for 25 or more weeks.
D
He must save for 12 or more weeks.
6

The outside temperature at midnight today in Polina’s hometown was 18 times degree F The temperature increases by 1 point 2 times degree F each hour over the next 15 hours. Polina’s school does not send students outside for recess if the outside temperature is 32 times degree F or lower. Recess at her school always starts on the half hour or hour. Which statement is true about recess at Polina’s school?

A
Only students who have recess at 11:30 a.m. or later may go outside.
B
Only students who have recess at 12:00 p.m. or later may go outside.
C
Only students who have recess at 11:00 a.m. or later may go outside.
D
Only students who have recess at 12:30 p.m. or later may go outside.
7

Which graph shows the solution set for negative 4 point 4 is greater than or equal to 1 point 6 x minus 3 point 6 ?

A
Image with description A number line ranges from negative 3 to 3 by one halves. Only integers are labeled. A closed circle is on the first tick mark to the right of negative 1. A ray is drawn from that circle pointing to the left.
B
Image with description A number line ranges from negative 3 to 3 by one halves. Only integers are labeled. A closed circle is on the first tick mark to the right of negative 1. A ray is drawn from that circle pointing to the right.
C
Image with description A number line ranges from negative 7 to negative 1 by one halves. Only integers are labeled. A closed circle is on negative 5. A ray is drawn from that circle pointing to the right.
D
Image with description A number line ranges from negative 7 to negative 1 by one halves. Only integers are labeled. A closed circle is on negative 5. A ray is drawn from that circle pointing to the left.
8

Yuto and Hila attempted to solve the same inequality. Their work is shown. Yuto’s Work Hila’s Work negative 2 thirds x plus 9 is greater than 7 negative 2 thirds x plus 9 is greater than 7 negative 2 thirds x plus 9 minus 9 is greater than 7 minus 9 negative 2 thirds x plus 9 plus 9 is greater than 7 plus 9 negative 2 thirds x is greater than negative 2 negative 2 thirds x is greater than 16 open paren negative 3 halves close paren times open paren negative 2 thirds x close paren is less than open paren negative 3 halves close paren times open paren negative 2 over 1 close paren open paren negative 3 halves close paren times open paren negative 2 thirds x close paren is less than open paren negative 3 halves close paren times open paren 16 over 1 close paren x is less than 3 x is less than negative 24 Which statement is true about the work shown above?

A
Hila is correct because she isolated the variable correctly and reversed the inequality symbol.
B
Hila is incorrect because she should not have reversed the inequality symbol.
C
Yuto is incorrect because he should not have reversed the inequality symbol.
D
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
9

Ling must spend no more than 40 point 0 0 dollars on decorations for a party. She has spent 10 point 0 0 dollars on streamers and wants to buy bags of balloons as well. Each bag of balloons costs 2 point 5 0 dollars The given inequality represents x , the number of bags she can buy given the spending limit and how much she has already spent on streamers. 10 plus 2 point 5 x is less than or equal to 40 Which best describes the number of bags of balloons she can buy?

A
She must buy 12 or more bags.
B
She can buy from 0 to 20 bags, but no more.
C
She must buy 20 or more bags.
D
She can buy from 0 to 12 bags, but no more.
10

Which graph shows the solution set for negative 5 halves x minus 3 is less than or equal to 2 ?

A
Image with description A number line ranges from negative 8 to 2 by ones. A closed circle is on negative 2. A ray is drawn from that circle pointing to the left.
B
Image with description A number line ranges from negative 8 to 2 by ones. A closed circle is on negative 2. A ray is drawn from that circle pointing to the right.
C
Image with description A number line ranges from negative 8 to 2 by ones. An open circle is on negative 2. A ray is drawn from that circle pointing to the left.
D
Image with description A number line ranges from negative 8 to 2 by ones. An open circle is on negative 2. A ray is drawn from that circle pointing to the right.

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Solving Two-Step Inequalities — Quiz Answers…