# Worksheet: Two-Step Linear Inequalities

In this worksheet, we will practice solving a linear inequality in two steps.

**Q1: **

Find the solution set of given that .

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- D

**Q2: **

Determine the solution set of , where .

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**Q3: **

Find the solution set of given that .

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- D

**Q4: **

Mrs. Williams tells her math class, “Five more than four times a number is more than 12.” Let represent the number and write an inequality that represents her statement.

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- E

**Q5: **

Given that , solve the inequality .

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**Q6: **

Solve the inequality in .

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**Q7: **

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

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- D

**Q8: **

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

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- E

**Q14: **

Determine the solution set of given that .

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- D

**Q15: **

Find the solution set of the inequality . Write your answer as an interval.

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**Q16: **

Find the solution set of given that .

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- D

**Q17: **

If , then .

**Q18: **

If , then .

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**Q19: **

Determine the solution set of given that .

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**Q21: **

Matthew needs to buy some clothes. The store’s parking lot has the shown sign outside.

Write an inequality for , the time in hours, that Matthew can park if he has only $8.25 in cash.

- A
- B
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- D
- E

Given that you must pay for whole hours of parking, use your inequality to find the maximum time that Matthew can park.

- A6 hours
- B5 hours
- C12 hours
- D9 hours
- E7 hours

**Q22: **

A hotel caters for large parties and events. They charge $300 for the hall and $15 per person for a lunchtime buffet.

Write an inequality that can be used to find , the number of people who can go to a party that was planned with a budget of .

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Use your inequality to find the maximum number of people.

**Q23: **

A candy store has a special offer: if you spend more than $15, you get a free chocolate drink. Gift boxes are $3 each, and chocolates are $2 per 50 g. Write an inequality to find , the weight of the chocolate you must buy with a gift box, if you are to receive a free chocolate drink.

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- E

**Q24: **

This number line describes the solution set to which of the following inequalities?

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- E