Answers7th Grade Math CR Summer SchoolSolving Two-Step Inequalities

Using Graphs to Solve Systems Answers

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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.
2
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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
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

Which graph shows the solution set for ?

Question illustration
A
A number line going from negative 8 to positive 2. An open circle is at negative 2. Everything to the left of the circle is shaded.
Option A
B
A number line going from negative 8 to positive 2. An open circle is at negative 2. Everything to the right of the circle is shaded.
Option B
C
A number line going from negative 8 to positive 2. A closed circle is at negative 2. Everything to the left of the circle is shaded.
Option C
D
A number line going from negative 8 to positive 2. A closed circle is at negative 2. Everything to the right of the circle is shaded.
Option D
5

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

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

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
7

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.
8

Savannah buys a $40 gift card to her favorite smoothie shop. Each smoothie costs $4. She wants to have at least $10 left on her card at the end of this month. The inequality below relates x, the number of smoothies she could buy between now and the end of this month with her gift card balance.Which best describes the number of smoothies Savannah can buy?

Question illustration
A
She can buy from 0 to 3 smoothies, but no more.
B
She can buy from 0 to 7 smoothies, but no more.
C
She can buy from 0 to 8 smoothies, but no more.
D
She can buy from 0 to 10 smoothies, but no more.
9

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.
10

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

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