Lesson Worksheet: Compound Linear Inequalities Mathematics

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?

  • 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‘₯

Q2:

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

Q3:

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

  • A
  • B
  • C
  • D

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

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

Q9:

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

Q10:

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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