Lesson Worksheet: Compound Linear Inequalities Mathematics

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


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

  • Aβˆ’8+π‘₯<7π‘₯+4≀16+π‘₯
  • Bβˆ’8+π‘₯β‰€βˆ’7π‘₯+4≀16+π‘₯
  • Cβˆ’8+π‘₯≀7π‘₯+4<16+π‘₯
  • Dβˆ’8+π‘₯≀7π‘₯βˆ’4≀16+π‘₯
  • Eβˆ’8+π‘₯≀7π‘₯+4≀16+π‘₯


How many integer solutions does the inequality 12<π‘₯<34 have?


Which of the following diagrams represents the solution set of the inequalities 3π‘₯βˆ’2<10 and π‘₯+2>3?

  • A
  • B
  • C
  • D


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.

  • A6<π‘₯<9
  • Bπ‘₯>9
  • C3<π‘₯<6
  • D3<π‘₯<9
  • Eπ‘₯>6


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 π‘Ž years. Write an inequality that describes the range of values of π‘Ž when a child must wear a seatbelt when sitting in the rear of the car.

  • A8<π‘Ž<18
  • Bπ‘Ž>18
  • C8<π‘Žβ‰€18
  • D8β‰€π‘Ž<18
  • Eπ‘Ž<18

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

  • A1<π‘Žβ‰€8
  • Bπ‘Ž<8
  • Cπ‘Ž>8
  • D1<π‘Ž<8
  • E1β‰€π‘Ž<8

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

  • A𝑀≀4
  • B𝑀>20
  • C𝑀β‰₯20
  • D𝑀≀20
  • E𝑀β‰₯4

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

  • A1<π‘Ž<4
  • B1β‰€π‘Ž<4
  • Cπ‘Ž<4
  • Dπ‘Ž>4
  • E1<π‘Žβ‰€4


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 𝑇 at which the two types of food can be stored together.

  • A17≀𝑇≀7
  • B0≀𝑇≀17
  • C7≀𝑇≀17
  • D7≀𝑇≀30
  • E0≀𝑇≀30


Natalie had $15 when she went to the cinema. She spent 𝑑dollars 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.

  • Aπ‘₯<22.1
  • Bπ‘₯>7.9
  • Cπ‘₯<15
  • Dπ‘₯<7.9
  • Eπ‘₯>22.1


Express the following symbolically: π‘₯ is greater than3 and less than18.

  • A3<π‘₯<18
  • B3>π‘₯>18
  • C3≀π‘₯β‰₯18
  • D3β‰₯π‘₯≀18


Students in a grade 4 class were asked the distances in miles, 𝑑, 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?

  • A0.75≀𝑑<6
  • B0.5≀𝑑<3
  • C0.25<𝑑≀3
  • D0.25≀𝑑<3
  • E0.75<𝑑≀3


Find all the values of π‘₯ that satisfy the inequality 15≀3π‘₯+3<21.

  • A6≀π‘₯<8
  • B18≀π‘₯<24
  • C9≀π‘₯<15
  • D12≀π‘₯<18
  • E4≀π‘₯<6

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