Answers7th Grade Math CR Summer SchoolSolving Two-Step Inequalities

Solving Two-Step Inequalities Answers

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1
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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.
2
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What is the solution to ?

Question illustration
A
x >
Option A
B
x <
Option B
C
x > 2
D
x < 2
3

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.
4

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.
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

Look at the two equations:-3x + 6 = 21-3x + 6 < 21Which statement best describes the process used to solve the equations?

A
In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality.
B
In both cases, divide by –3 on both sides, but reverse the inequality sign when doing that for the inequality.
C
The process is exactly the same for solving the equation and solving the inequality.
D
The process for solving the equation is entirely different from solving the inequality.
7

Aiden has $15.00 on his copy card. Each time he uses the card to make a photocopy, $0.06 is deducted from his card. Aiden wants to be sure that there will be at least $5.00 left on his card when he is finished. The inequality below relates x, the number of copies he can make, with his copy card balance.What is the maximum number of copies Aiden can make?

Question illustration
A
60
B
83
C
166
D
250
8

What is the solution to ?

Question illustration
A
x greater-than-or-equal-to 0.2
Option A
B
x greater-than-or-equal-to 0.6
Option B
C
x greater-than-or-equal-to 1.8
Option C
D
x greater-than-or-equal-to 2.5
Option D
9

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.
10

Which graph shows the solution set for ?

Question illustration
A
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded.
Option A
B
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the right of the circle is shaded.
Option B
C
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the left of the circle is shaded.
Option C
D
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Option D

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