# Worksheet: Introduction to Inequalities

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

**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
- C
- D
- 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
- C
- D
- E

**Q13: **

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

- A
- B
- C
- D

**Q14: **

Amelia 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