Worksheet: Writing Inequalities

In this worksheet, we will practice identifying and writing simple inequalities to represent verbal expressions.

Q1:

Sameh walked for 29 minutes before reaching the university campus. He took at least another 5 minutes to reach the lecture hall. Write an inequality that represents the amount of time it took Sameh to reach the lecture hall.

  • A
  • B
  • C
  • D
  • E

Q2:

Samar was able to clean more than 3 7 of her flat after her friends came over and left. Write an inequality to represent the fraction of the flat that she still has left to clean.

  • A π‘₯ < 3 7
  • B π‘₯ > 4 7
  • C π‘₯ > 3 7
  • D π‘₯ < 4 7
  • E π‘₯ β‰₯ 4 7

Q3:

Write an expression for 𝑐 which means that it is less than or equal to 3.

  • A 𝑐 < 3
  • B 𝑐 > 3
  • C 𝑐 β‰₯ 3
  • D 𝑐 ≀ 3

Q4:

Write an inequality which describes the following sentence: The subscription fee is no more than $74.

  • A π‘₯ < 7 4
  • B π‘₯ > 7 4
  • C π‘₯ β‰₯ 7 4
  • D π‘₯ ≀ 7 4

Q5:

Write an inequality which describes the following sentence: Karim drives more than 7 400 miles per year.

  • A
  • B
  • C
  • D

Q6:

An Olympic athlete is helping her niece train. The athlete can run short distances at 9 m/s, and her niece can run short distances at 7 m/s. The athlete gives her niece a 2-second head start in a sprint race, and her niece runs for 𝑑 seconds.

Write an inequality for the values of 𝑑 , when the athlete is behind her niece. Assume that they run at steady speeds the entire race.

  • A 𝑑 < 7
  • B 𝑑 > 9
  • C 𝑑 > 7
  • D 𝑑 < 9
  • E 𝑑 β‰₯ 9

Q7:

The number of cupcakes a cafΓ© sells each day is 𝑐 . To make a profit, the cafΓ© must sell more than 100 cupcakes every day. Write an inequality that describes when the cafΓ© starts to make a profit.

  • A 𝑐 ≀ 1 0 1
  • B 𝑐 < 1 0 0
  • C 𝑐 ≀ 1 0 0
  • D 𝑐 > 1 0 0
  • E 𝑐 > 1 0 1

Q8:

A school trip will run if at least 40 students want to go. Write an inequality to represent the situation, using 𝑆 to represent the number of students.

  • A 𝑆 < 4 0
  • B 𝑆 > 4 0
  • C 𝑆 ≀ 4 0
  • D 𝑆 β‰₯ 4 0
  • E 𝑆 β‰₯ 4 1

Q9:

The sign shown is on the railings at π‘Ž toddlers’ play area.

Letting π‘Ž be the allowed age of a child in the play area, write an inequality that represents the rule on the sign.

  • A π‘Ž ≀ 5
  • B π‘Ž > 5
  • C π‘Ž β‰₯ 6
  • D π‘Ž < 5
  • E π‘Ž ≀ 4

Q10:

A corner shop has the sign β€œNo more than 4 school children in the shop at any time.” Write an inequality that represents the statement on the shop’s sign, using 𝑛 to represent the number of school children in the shop.

  • A 𝑛 > 3
  • B 𝑛 < 4
  • C 𝑛 β‰₯ 4
  • D 𝑛 ≀ 4
  • E 𝑛 ≀ 3

Q11:

Which of the following is an inequality?

  • A 1 2 𝑛 + 4 2
  • B 7 βˆ’ 2 ( π‘₯ βˆ’ 1 ) = 4
  • C 2 π‘₯ βˆ’ 7 ≀ 5

Q12:

Rewrite the statement β€œ 𝑦 is between 8 1 0 a n d ” using < , ≀ , > , or β‰₯ .

  • A 8 < 𝑦 > 1 0
  • B 1 0 < 𝑦 ≀ 8
  • C 8 > 𝑦 < 1 0
  • D 8 < 𝑦 < 1 0
  • E 8 ≀ 𝑦 ≀ 1 0

Q13:

Which of the following expressions ensures that π‘₯ is negative for all the possible values of π‘₯ ∈ ℝ ?

  • A π‘₯ = 0
  • B π‘₯ β‰₯ 0
  • C π‘₯ > 2 3
  • D π‘₯ ≀ βˆ’ 9

Q14:

Sarah needs to travel by train, and she’s preparing her journey to the train station. It takes her 7 minutes to walk to the bus stop from home. There is a bus every 12 minutes, and the bus journey to the train station usually lasts 20 minutes. After that, she needs at most 4 minutes to get off the bus and reach her train.

Assuming her bus is not delayed, write an inequality to describe the time, , in minutes, it takes her to travel to the train station by bus.

  • A
  • B
  • C
  • D
  • E

Given that her train departs at 14.47, at what time should she leave home to make sure that she catches the train?

  • Abefore 14.04
  • Bafter 14.16
  • Cbetween 14.04 and 14.16.
  • Dat 14.16
  • Eafter 14.04

Q15:

Write an expression for 𝑦 which means that it is greater than or equal to 4.

  • A 𝑦 < 4
  • B 𝑦 ≀ 4
  • C 𝑦 > 4
  • D 𝑦 β‰₯ 4

Q16:

Write an expression for 𝑛 which means that it is less than 3.

  • A 𝑛 ≀ 3
  • B 𝑛 > 3
  • C 𝑛 β‰₯ 3
  • D 𝑛 < 3

Q17:

Write an expression for 𝑏 which means that it is greater than 5.

  • A 𝑏 β‰₯ 5
  • B 𝑏 < 5
  • C 𝑏 ≀ 5
  • D 𝑏 > 5

Q18:

Write an expression for 𝑛 which means that it is greater than 5.

  • A 𝑛 β‰₯ 5
  • B 𝑛 < 5
  • C 𝑛 ≀ 5
  • D 𝑛 > 5

Q19:

Write an expression for 𝑏 which means that it is less than 1.

  • A 𝑏 ≀ 1
  • B 𝑏 > 1
  • C 𝑏 β‰₯ 1
  • D 𝑏 < 1

Q20:

Write an expression for π‘Ž which means that it is greater than or equal to 9.

  • A π‘Ž < 9
  • B π‘Ž ≀ 9
  • C π‘Ž > 9
  • D π‘Ž β‰₯ 9

Q21:

Write an expression for 𝑦 which means that it is less than or equal to 3.

  • A 𝑦 < 3
  • B 𝑦 > 3
  • C 𝑦 β‰₯ 3
  • D 𝑦 ≀ 3

Q22:

Write an expression for π‘₯ which means that it is greater than 5.

  • A π‘₯ β‰₯ 5
  • B π‘₯ < 5
  • C π‘₯ ≀ 5
  • D π‘₯ > 5

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