Worksheet: Writing Inequalities

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

Q1:

Matthew 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 Matthew to reach the lecture hall.

  • A π‘₯ ≀ 3 4
  • B π‘₯ β‰₯ 2 4
  • C π‘₯ ≀ 2 9
  • D π‘₯ ≀ 2 4
  • E π‘₯ β‰₯ 3 4

Q2:

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

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

Q4:

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

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

Q5:

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

  • A π‘₯ β‰₯ 7 , 4 0 0
  • B π‘₯ < 7 , 4 0 0
  • C π‘₯ > 7 , 4 0 0
  • D π‘₯ ≀ 7 , 4 0 0

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

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

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

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

Q10:

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

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

Q11:

Which of the following is an inequality?

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

Q12:

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

  • A 8 ≀ 𝑦 ≀ 1 0
  • B 8 > 𝑦 < 1 0
  • C 8 < 𝑦 > 1 0
  • D 1 0 < 𝑦 ≀ 8
  • 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‘₯ > 2 3
  • B π‘₯ ≀ βˆ’ 9
  • C π‘₯ = 0
  • D π‘₯ β‰₯ 0

Q14:

Emma needs to travel by train, and she is 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, 𝑑 , in minutes, it takes her to travel to the train station by bus.

  • A 𝑑 ≀ 4 3
  • B 𝑑 ≀ 3 5
  • C 𝑑 β‰₯ 4 3
  • D 𝑑 < 4 3

Given that her train departs at 14:47, at what time should she leave home to make sure that she catches the train?

  • AAfter 14:16
  • BBefore 14:04
  • CAfter 14:04
  • DAt 14:16
  • EBetween 14:04 and 14:16

Q15:

Write an expression for 𝑐 which means that it is less than or equal to 5.

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

Q16:

Write an expression for 𝑐 which means that it is less than or equal to 1.

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

Q17:

Write an expression for π‘š which means that it is less than or equal to 2.

  • A π‘š > 2
  • B π‘š ≀ 2
  • C π‘š < 2
  • D π‘š β‰₯ 2

Q18:

Write an expression for 𝑏 which means that it is less than or equal to 4.

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

Q19:

Write an expression for 𝑦 which means that it is less than or equal to 6.

  • A 𝑦 > 6
  • B 𝑦 < 6
  • C 𝑦 ≀ 6
  • D 𝑦 β‰₯ 6

Q20:

Write an expression for 𝑛 which means that it is less than or equal to 7.

  • A 𝑛 β‰₯ 7
  • B 𝑛 ≀ 7
  • C 𝑛 < 7
  • D 𝑛 > 7

Q21:

Write an expression for 𝑛 which means that it is less than or equal to 8.

  • A 𝑛 > 8
  • B 𝑛 < 8
  • C 𝑛 ≀ 8
  • D 𝑛 β‰₯ 8

Q22:

Given that π‘₯ ∈ [ βˆ’ 3 5 , ∞ ) , which of the following inequalities holds?

  • A π‘₯ < βˆ’ 3 5
  • B π‘₯ ≀ βˆ’ 3 5
  • C π‘₯ > βˆ’ 3 5
  • D π‘₯ β‰₯ βˆ’ 3 5

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