# 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

Q2:

Solve and .

• Ano solution
• 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

Q5:

Solve and .

• A
• B
• C
• D
• E

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?

• Ainfinite
• B3
• C2
• D0

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 ,

Q11:

Solve and .

• A
• B
• C
• D
• E

Q12:

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

• A
• B
• C
• D

Q13:

Emma has 6 cats as pets. One of her cats, Natalie, is pregnant. Write an inequality for the number of cats Emma will have if Natalie gives birth to fewer than 3 kittens.

• A
• B
• C
• D
• E

Q14:

A state’s 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 child’s 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

Q22:

Given that , find the greatest possible value of .

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