AnswersSC-Mathematics 6Multiplication and Division Inequalities

Solving Two-Step Inequalities Answers

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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.
2
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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.
3

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
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

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.
7

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.
8

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
9

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
10

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.
11

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.
12

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.
13

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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