# 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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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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• E

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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Q9:

Solve .

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Q10:

Solve the inequality for .

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• E

Q11:

Solve the following inequality: .

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• E

Q12:

Write the set of all integer solutions to .

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Q13:

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Q14:

Determine the solution set of given that .

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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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Q17:

If , then .

Q18:

If , then .

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Q19:

Determine the solution set of given that .

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Q20:

Michael wants to purchase a precision balance for \$340. He has already saved \$113 and can save \$28 every week. Write an inequality that can be used to determine the number of weeks left for Michael to save at least \$340.

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• E

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.

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• 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? • A
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• E

Q25:

Solve the following inequality: .

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• E