# Worksheet: Compound Linear Inequalities

In this worksheet, we will practice solving compound linear inequalities by applying inverse operations.

**Q1: **

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

- A
- B
- C
- D
- E

**Q3: **

Find the solution set of , where .

- A
- B
- C
- D

**Q4: **

Find the solution set of given that .

- A
- B
- C
- D

**Q6: **

Find the solution set of , where .

- A
- B
- C
- D

**Q7: **

Given that , solve the inequality .

- A
- B
- C
- D
- E

**Q8: **

How many integer solutions does the inequality have?

**Q9: **

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

- A
- B
- C
- D

**Q10: **

The solution set of is . What are the values of and ?

- A,
- B,
- C,
- D,
- E,

**Q12: **

Which of the following diagrams represents the solution set of the inequalities and ?

- A
- B
- C
- D

**Q14: **

A stateβs regulations to ensure child passenger safety are as follows:

- From the age of 18, there is no legal requirement for passengers traveling in the back seat of a car to use a seat belt.
- Children under 1 year of age and children weighing less than 20 lb are required to be in a rear-facing seat.
- Children age 1 to age 3 years (inclusive) and at least 20 lb in weight are required to be in a forward-facing seat.
- Children age 4 to age 7 years (inclusive) are required to be in a forward-facing car seat or a booster seat.
- Children at 8 years old or above are required to use standard vehicle safety belt.

The age of a child is years. Write an inequality that describes the range of values of when a child must wear a seatbelt when sitting in the rear of the car.

- A
- B
- C
- D
- E

The age of a child who weighs over 20 lb is years. Write an inequality that describes the range of values of when the child must use a forward-facing car seat or booster seat.

- A
- B
- C
- D
- E

A child is under 4 years old. The childβs weight in pounds is . Write an inequality that describes the range of values of , for which the child may travel in a forward-facing seat.

- A
- B
- C
- D
- E

A child weighs more than 20 pounds. Their age is . Write an inequality that describes the range of ages for which they must use a forward-facing seat.

- A
- B
- C
- D
- E

**Q15: **

A warehouse stores two types of food. The first needs to be stored at a temperature between 0 and 17 degrees. As for the second, it needs to be kept at a temperature between 7 to 30 degrees. Find the range of the temperature at which the two types of food can be stored together.

- A
- B
- C
- D
- E

**Q16: **

Natalie had $15 when she went to the cinema. She spent on the ticket and $7.10 on the popcorn. Write an inequality that represents the amount of money Natalie had when she left the cinema.

- A
- B
- C
- D
- E

**Q17: **

Express the following symbolically: is greater than and less than.

- A
- B
- C
- D

**Q18: **

Students in a grade 4 class were asked the distances in miles, , which they travel to get to school. All of the students traveled farther than a quarter of a mile, and no one traveled farther than 3 miles. Which of the following inequalities represents the range of distances traveled to school?

- A
- B
- C
- D
- E

**Q19: **

Find all the values of that satisfy the inequality

- A
- B
- C
- D
- E

**Q20: **

Find all the values of that satisfy the compound inequality

- A
- B
- C
- D
- E

**Q21: **

Find all the values of that satisfy or .

- A or
- B or
- C or
- D or
- E or

**Q23: **

Given that is a whole number and , what are the possible values of ?

- A
- B
- C
- D

**Q24: **

Find the solution set of , where .

- A
- B
- C
- D

**Q25: **

Find the solution set of , where .

- A
- B
- C
- D