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Worksheet: Writing Compound Inequalities

Q1:

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 π‘₯ > 6
  • B π‘₯ > 9
  • C 3 < π‘₯ < 6
  • D 6 < π‘₯ < 9
  • E 3 < π‘₯ < 9

Q2:

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

  • A 8 < π‘Ž ≀ 1 8
  • B 8 < π‘Ž < 1 8
  • C π‘Ž < 1 8
  • D 8 ≀ π‘Ž < 1 8
  • E π‘Ž > 1 8

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

  • A 1 ≀ π‘Ž < 8
  • B π‘Ž < 8
  • C 1 < π‘Ž ≀ 8
  • D 1 < π‘Ž < 8
  • E 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.

  • A 𝑀 ≀ 4
  • B 𝑀 > 2 0
  • C 𝑀 β‰₯ 2 0
  • D 𝑀 ≀ 2 0
  • E 𝑀 β‰₯ 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.

  • A 1 ≀ π‘Ž < 4
  • B π‘Ž > 4
  • C π‘Ž < 4
  • D 1 < π‘Ž < 4
  • E 1 < π‘Ž ≀ 4

Q3:

When three times a number is subtracted from nine, the result is no more than when the sum of the number and five is divided by two.

Write an inequality to represent the statement above. Let π‘₯ represent the number.

  • A 9 βˆ’ 3 π‘₯ > π‘₯ + 9 2
  • B 9 βˆ’ 3 π‘₯ < π‘₯ + 5 2
  • C 3 π‘₯ βˆ’ 9 < π‘₯ + 5 2
  • D 9 βˆ’ 3 π‘₯ ≀ π‘₯ + 5 2
  • E 3 π‘₯ βˆ’ 9 > π‘₯ + 5 2

Q4:

Use the fact that the perimeter of the equilateral triangle is more than the perimeter of the rectangle to write an inequality in π‘₯ .

  • A ( π‘₯ + 2 ) β‰₯ 4 π‘₯ βˆ’ 1 2
  • B 3 ( π‘₯ + 2 ) < 4 π‘₯ βˆ’ 1 2
  • C ( π‘₯ + 2 ) ≀ 3 π‘₯ βˆ’ 7
  • D 3 ( π‘₯ + 2 ) > 4 π‘₯ βˆ’ 1 2
  • E 3 ( π‘₯ + 2 ) > 2 π‘₯ βˆ’ 6

Q5:

Which of these scenarios best fits the inequality 7 5 > 6 π‘₯ + 4 ?

  • A You are trying to earn 75 points in a game and want to know how many levels you need if you earn 6 points per level but lose 4 points when you come across a gremlin.
  • B You need to earn more than $ 7 5 and want to know how many lawns you would have to mow if you earned $ 6 per lawn but spent $ 4 on gas.
  • C You have earned 75 tickets at an arcade and your friend has 4 tickets and you want to know how many prizes you can get if each prize costs 6 tickets.
  • D You go shopping for school clothes with a $ 7 5 budget and want to see how many $ 6 shirts you can buy after paying $ 4 for bus transportation.

Q6:

Danielis making shakers for a kindergarten music class. It takes him 5 minutes to get the yogurt pots, lentils, glue, and glitter out and at least 3 minutes to make and decorate one shaker. He has three-quarters of an hour to make some shakers. Write an inequality for 𝑛 , the number of shakers he can make in that time.

  • A 3 + 5 𝑛 ≀ 4 5
  • B 5 + 3 𝑛 β‰₯ 4 5
  • C 5 + 3 𝑛 ≀ 0 . 7 5
  • D 5 + 3 𝑛 ≀ 4 5
  • E 5 + 3 𝑛 β‰₯ 0 . 7 5

Q7:

Rewrite the statement β€œ1 is greater than or equal to ” using , , , or .

  • A
  • B
  • C
  • D

Q8:

There are some pencils and rulers in a desk organizer. Altogether, there are fewer than 20 items. Let 𝑝 be the number of pencils and π‘Ÿ the number of rulers.

Write a relationship that connects 𝑝 and π‘Ÿ .

  • A 𝑝 + π‘Ÿ = 2 0
  • B 𝑝 + π‘Ÿ > 2 0
  • C 𝑝 < 2 0 + π‘Ÿ
  • D 𝑝 + π‘Ÿ < 2 0
  • E π‘Ÿ < 2 0 + 𝑝

Q9:

The perimeter of the square is not less than the perimeter of the rectangle.

Write an inequality for the value of 𝐴 , the area of the square.

  • A 𝐴 β‰₯ 5 0
  • B 𝐴 > 2 5
  • C 𝐴 < 5 0
  • D 𝐴 ≀ 2 5
  • E 𝐴 ≀ 3 0

Q10:

Write an inequality to describe the following sentence: The offer is valid for any item that costs less than $6.

  • A π‘₯ ≀ 6
  • B π‘₯ > 6
  • C π‘₯ β‰₯ 6
  • D π‘₯ < 6

Q11:

A warehouse stores two types of food. The first needs to be stored at a temperature between βˆ’ 2 and 4 degrees. As for the second, it needs to be kept at a temperature between 1 to 22 degrees. Find the range of the temperature 𝑇 at which the two types of food can be stored together.

  • A βˆ’ 2 ≀ 𝑇 ≀ 2 2
  • B 1 ≀ 𝑇 ≀ 2 2
  • C βˆ’ 2 ≀ 𝑇 ≀ 4
  • D 1 ≀ 𝑇 ≀ 4
  • E 4 ≀ 𝑇 ≀ 1

Q12:

James went shopping with $40 in his wallet. He bought a pair of jeans for $22. He is now looking for a shirt. Let 𝑠 represent the price of the shirt in dollars. Which of the following describes the condition on 𝑠 for James to be able to buy the shirt?

  • A 𝑠 = 4 0 βˆ’ 2 2
  • B 𝑠 < 4 0 βˆ’ 2 2
  • C 𝑠 ≀ 4 0 + 2 2
  • D 𝑠 ≀ 4 0 βˆ’ 2 2
  • E 𝑠 < 4 0 + 2 2

Q13:

Natalie had $15 when she went to the cinema. She spent 𝑑 dollars 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 π‘₯ < 2 2 . 1
  • B π‘₯ > 7 . 9
  • C π‘₯ > 2 2 . 1
  • D π‘₯ < 7 . 9
  • E π‘₯ < 1 5

Q14:

Mr. Benjamin tells his class, β€œTwo more than ten times a number is at least 50.” Let π‘₯ represent the number, and write an inequality to represent his statement.

  • A 1 0 π‘₯ + 2 ≀ 5 0
  • B 1 0 π‘₯ + 2 > 5 0
  • C 2 π‘₯ + 1 0 > 5 0
  • D 1 0 π‘₯ + 2 β‰₯ 5 0
  • E 2 π‘₯ + 1 0 < 5 0

Q15:

The length of a rectangle is nine more than its width; the area of the rectangle is no more than 20. Write an inequality for the area of the rectangle, 𝐴 , in terms of the width, 𝑀 .

  • A 𝑀 ( 𝑀 βˆ’ 9 ) > 2 0
  • B 𝑀 ( 𝑀 + 9 ) β‰₯ 2 0
  • C 𝑀 ( 𝑀 βˆ’ 9 ) β‰₯ 2 0
  • D 𝑀 ( 𝑀 + 9 ) ≀ 2 0
  • E 𝑀 ( 2 𝑀 + 9 ) β‰₯ 2 0

Q16:

Scarlett and Madison are planning a party. CDs for the karaoke machine cost $5 each, and they will spend $3.50 per person on soft drinks and party food. They have a budget of $100, and they want to buy 2 new karaoke CDs. Write an inequality to determine the possible values of 𝑛 , the number of people that can go to the party.

  • A 7 . 5 𝑛 + 5 ≀ 1 0 0
  • B 3 . 5 𝑛 + 2 ≀ 1 0 0
  • C 3 . 5 𝑛 + 2 Γ— 5 β‰₯ 1 0 0
  • D 3 . 5 𝑛 + 2 Γ— 5 ≀ 1 0 0
  • E 7 . 5 𝑛 + 2 β‰₯ 1 0 0

Q17:

Express the following symbolically: π‘₯ is greater than 3 and less than 1 8 .

  • A 3 ≀ π‘₯ β‰₯ 1 8
  • B 3 > π‘₯ > 1 8
  • C 3 β‰₯ π‘₯ ≀ 1 8
  • D 3 < π‘₯ < 1 8

Q18:

A library offers two types of notebooks; the price of the first is 10.5 LE and the second is 15 LE. If David does not want to spend more than 41 LE, express a relation that shows how many notebooks he can buy.

  • A
  • B
  • C
  • D
  • E

Q19:

Natalie had a history examination. She had to plan and write 3 essays in 2 hours. Her total planning time was 25 minutes and she spent the same amount of time writing each essay.

Given that she had some time left at the end to check her work, write an inequality to find 𝑑 , the maximum time she could have spent on each essay.

  • A 2 5 + 3 𝑑 < 2
  • B 2 5 + 3 𝑑 > 1 2 0
  • C 2 5 + 3 𝑑 ≀ 2 4 0
  • D 2 5 + 3 𝑑 < 1 2 0
  • E 3 + 2 5 𝑑 ≀ 1 2 0

Q20:

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?

  • A 0 . 7 5 < 𝑑 ≀ 3
  • B 0 . 2 5 ≀ 𝑑 < 3
  • C 0 . 7 5 ≀ 𝑑 < 6
  • D 0 . 2 5 < 𝑑 ≀ 3
  • E 0 . 5 ≀ 𝑑 < 3