Solving Two-Step Inequalities Answers

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Felicia had $80 when she went to a music store that charges $18 for each CD. She needs to have no less than $20 in her wallet when she leaves the store so she has enough money to buy gas for the ride home. Which shows a possible number of CDs she could buy? Select three options.

A
1
B
2
C
3
D
4
E
5
2
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The outside temperature at midnight today in Polina’s hometown was . The temperature increases by each hour over the next 15 hours. Polina’s school does not send students outside for recess if the outside temperature is or lower. Recess at her school always starts on the half hour or hour. Which statement is true about recess at Polina’s school?

Question illustration
A
Only students who have recess at 11:00 a.m. or later may go outside.
B
Only students who have recess at 11:30 a.m. or later may go outside.
C
Only students who have recess at 12:00 p.m. or later may go outside.
D
Only students who have recess at 12:30 p.m. or later may go outside.
3

Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below.What errors did Parul make? Select three options.

Question illustration
A
She added 3.5 to both sides when she should have subtracted.
B
She should have divided both sides by as her first step.
Option B
C
She divided one side by -5 while multiplying the other side by -5.
D
She did not change the > symbol to a < symbol.
E
She used a closed circle instead of an open circle on the number line.
4

Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 per job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.Which best describes the restrictions on the jobs Deepak will accept?

Question illustration
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.
5

Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.What is the greatest number of bracelets she could buy?

Question illustration
A
20
B
30
C
63
D
83
6

Yuto and Hila attempted to solve the same inequality. Their work is shown below.Yuto’s WorkHila’s WorkWhich statement is true about the work shown above?

Question illustration
A
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
B
Yuto is incorrect because he should not have reversed the inequality symbol.
C
Hila is correct because she isolated the variable correctly and reversed the inequality symbol.
D
Hila is incorrect because she should not have reversed the inequality symbol.
7

Soro bought a $50.00 bus card at the beginning of the week. Each bus ride costs $2.50. He needs to have at least $20.00 on his card at the end of this month.To determine how many bus rides he can take between now and the end of this month, Soro wrote and solved the following inequality:What error, if any, did Soro make when writing or solving this inequality?

Question illustration
A
Soro’s original inequality should have been .
Option A
B
Soro should have added 2.5 to each side for his first step.
C
Soro should have reversed the inequality symbol when using the division property of inequality.
D
Soro’s work shows no errors.
8

What is the solution to ?

Question illustration
A
x >
Option A
B
x <
Option B
C
x > 2
D
x < 2
9

Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.Which best describes the number of bags of balloons she can buy?

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

Raul has $460 in his checking account. Each month, $45 is automatically deducted from his account to pay for his cell phone plan. He makes no other deposits or withdrawals. He wants to always have more than $100 in his account. What is the greatest number of months he can pay for his cell phone and still have more than $100 in his account?

A
7 months
B
8 months
C
9 months
D
10 months

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