AnswersSRC 2022 MJ Grade 8 Pre-Algebra Q1Solving Multistep Equations with Variables on Both Sides

Solving Two-Step Inequalities Answers

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1
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What is the first step in solving c ?

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A
Add to both sides.
Option A
B
Subtract from both sides.
Option B
C
Divide both sides by –5.
Option C
D
Multiply both sides by –5.
Option D
2
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Which did you include in your solution? Check all that apply.

A
The inequality representing the situation is 0.5x + 3 < 10.
B
Use inverse operations and properties of inequality to solve.
C
Find that x < 14.
D
Carl lives 15 miles from home, so he will take a bus.
3

Solve –9.4 1.7x + 4.2.

Question illustration
A
x –8
Option A
B
x 8
Option B
C
x –8
Option C
D
x 8
Option D
4

Solve . x >

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Answer:

9/5

7

Question text not available

Answers:
.:subtract 47.5 from both sides
.:divide both sides by 4.5
snacks.:3
9

The second step is to add 4.5 to both sidessubtract 4.5 from both sidesmultiply both sides by 4.5 ✔ divide both sides by 4.5.

A
add 4.5 to both sides
B
subtract 4.5 from both sides
C
multiply both sides by 4.5
D
✔ divide both sides by 4.5
11

A taxi charges a flat rate of $3.00, plus an additional $0.50 per mile. Carl will only take the taxi home if the cost is under $10, otherwise he will take a bus. Carl is 15 miles from home. Explain how to write and solve an inequality to determine if Carl will take the taxi or a bus.

Answer:

To determine if Carl will take the taxi, let x represent the number of miles. The inequality for the cost is 0.50x + 3 < 10. To solve, first subtract 3 from both sides of the inequality to get 0.50x < 7. Next, divide both sides by 0.50 to find that x < 14. This means Carl can only afford the taxi if the trip is less than 14 miles. Since Carl is 15 miles from home, he will take the bus.

12

Review Jamie’s work. What was her error?

A
Jamie should have used the less than or equal to sign when writing the inequality.
B
Jamie should have reversed the inequality when using the division property of inequality.
C
Jamie should have added 500 to both sides.
D
Jamie should have started by dividing by –30.

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