# Worksheet: Introduction to Inequalities

In this worksheet, we will practice interpreting and writing simple inequalities to represent verbal expressions.

**Q4: **

Write an inequality which describes the following sentence: The subscription fee is no more than $74.

- A
- B
- C
- D

**Q5: **

Write an inequality which describes the following sentence: David drives more than 7,400 miles per year.

- A
- B
- C
- D

**Q6: **

An Olympic athlete is helping her niece train. The athlete can run short distances at 9 m/s, and her niece can run short distances at 7 m/s. The athlete gives her niece a 2-second head start in a sprint race, and her niece runs for seconds.

Write an inequality for the values of , when the athlete is behind her niece. Assume that they run at steady speeds the entire race.

- A
- B
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- D
- E

**Q7: **

The number of cupcakes a cafΓ© sells each day is . To make a profit, the cafΓ© must sell more than 100 cupcakes every day. Write an inequality that describes when the cafΓ© starts to make a profit.

- A
- B
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- E

**Q8: **

A field trip will run if at least 40 students want to go. Write an inequality to represent the situation, using to represent the number of students.

- A
- B
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- E

**Q9: **

The sign shown is on the railings at toddlersβ play area.

Letting be the allowed age of a child in the play area, write an inequality that represents the rule on the sign.

- A
- B
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- D
- E

**Q10: **

A corner store has the sign βNo more than 4 school children in the store at any time.β Write an inequality that represents the statement on the storeβs sign, using to represent the number of school children in the store.

- A
- B
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- D
- E

**Q11: **

Which of the following is an inequality?

- A
- B
- C

**Q12: **

Rewrite the statement β is between 8 and 10β using , , , or .

- A
- B
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- E

**Q13: **

Which of the following expressions ensures that is negative for all the possible values of ?

- A
- B
- C
- D

**Q14: **

Emma needs to travel by train, and she is preparing her journey to the train station. It takes her 7 minutes to walk to the bus stop from home. There is a bus every 12 minutes, and the bus journey to the train station usually lasts 20 minutes. After that, she needs at most 4 minutes to get off the bus and reach her train.

Assuming her bus is not delayed, write an inequality to describe the time, , in minutes, it takes her to travel to the train station by bus.

- A
- B
- C
- D

Given that her train departs at 14:47, at what time should she leave home to make sure that she catches the train?

- ABetween 14:04 and 14:16
- BAfter 14:04
- CBefore 14:04
- DAfter 14:16
- EAt 14:16

**Q23: **

What is the name of the set of all values that satisfy a given equation or inequality?

- Athe solving set
- Bthe substitution set
- Cthe solution set
- Dthe data set
- Ethe satisfaction set

**Q24: **

Complete using , , or : if , then .

- A
- B
- C

**Q25: **

Complete using , , or : if , , then .

- A
- B
- C