# Worksheet: Multistep Inequalities

In this worksheet, we will practice solving multistep inequalities.

**Q2: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q3: **

Find the solution set of the inequality in . Give your answer in interval notation.

- A
- B
- C
- D

**Q4: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q5: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q6: **

Solve the inequality in .

- A
- B
- C
- D

**Q7: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q8: **

Given that , solve the inequality .

- A
- B
- C
- D
- E

**Q9: **

Solve the inequality in .

- A
- B
- C
- D

**Q10: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q11: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q12: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q13: **

Solve the inequality in .

- A
- B
- C
- D
- E

**Q14: **

Find the solution set of the inequality in . Give your answer in interval notation.

- A
- B
- C
- D
- E

**Q15: **

Suppose that . Solve the inequality .

- A
- B
- C
- D
- E

**Q16: **

Given that , solve the inequality .

- A
- B
- C
- D
- E

**Q17: **

When hired at a new job selling electronics, you are given two pay options:

- Option A: a base salary of a year with a commission of of your sales.
- Option B: a base salary of a year with a commission of of your sales.

How many dollarsβ worth of electronics would you need to sell for Option A to produce a larger income?

- AMore than worth of electronics
- BMore than worth of electronics
- CMore than worth of electronics
- DMore than worth of electronics

**Q18: **

When hired at a new job selling electronics, you are given two pay options:

- Option A: a base salary of a year with a commission of of your sales
- Option B: a base salary of a year with a commission of of your sales

How many dollarsβ worth of electronics would you need to sell for option A to produce a larger income?

- Amore than worth of electronics
- Bmore than worth of electronics
- Cmore than worth of electronics
- Dmore than worth of electronics

**Q20: **

William and Daniel are competing on a quiz app. William has 400 points and is losing 2 points per minute; Daniel has 250 points and is winning 10 points per minute.

Write an inequality which can be used to find , the amount of time for which William has no fewer points than Daniel.

- A
- B
- C
- D
- E

Use your inequality to find the time when Daniel catches up with William. Assume that points are won or lost at a constant rate.

- A6 minutes
- B minutes
- C minutes
- D minutes
- E14 minutes

**Q21: **

A cell phone company offers the following two plans:

- Plan A: $20 per month and $1 for every one hundred texts.
- Plan B: $50 per month with free, unlimited texts.

How many texts would you need to send per month for plan B to save you money?

- AMore than 3,000
- BLess than 3,000
- CLess than 30
- DMore than 30

**Q23: **

You just got a new job in retail and you are given two options for your earnings:

**Option 1:** Base salary of $15,000 per year plus a commission of of your sales.

**Option 2:** Base salary of $18,000 per year plus a commission of of your sales.

How much money in sales would you need to make in order for Option 1 to yield a higher income than Option 2?

- AMore than $137,500
- BMore than $12,500
- CMore than $75,000
- DMore than $18,000

**Q24: **

A moving company charges a flat rate of $150 and an additional $5 for each box. If a taxi service charged $20, for how many boxes would it be cheaper to move with the taxi service than with the moving company?

- Amore than 6 boxes
- Bonly at 10 boxes
- Cmore than 10 boxes
- Dless than 10 boxes
- Eless than 6 boxes