# Worksheet: Multistep Inequalities

In this worksheet, we will practice solving multistep inequalities.

Q1:

Given that , write the solution set of .

• A
• B
• C
• D
• E

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 dollars’ 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 dollars’ 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

Q19:

A cell phone company offers the following two plans:

• Plan A: \$15 per month and \$2 for every 300 texts.
• Plan B: \$25 per month and \$0.50 for every 100 texts.

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

• ALess than 60
• BMore than 6,000
• CMore than 60
• DLess than 6,000

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

Q22:

Sophia finds two landscape gardeners online: the first charges a fixed fee of \$20 per job plus \$15 per hour for labor, while the second charges a fixed fee of \$90 but only \$5 per hour for labor. After how many hours will the second gardener be cheaper than the first?

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

Q25:

The cost of producing “doomflots” is \$325 for equipment plus another \$32 for materials and labor for each one produced. How many “doomflots” need to be produced such that the average cost per “doomflot” is less than \$50?