Worksheet: Introduction to Inequalities

In this worksheet, we will practice interpreting 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.

  • Aπ‘₯≀24
  • Bπ‘₯β‰₯24
  • Cπ‘₯≀29
  • Dπ‘₯β‰₯34
  • Eπ‘₯≀34

Q2:

Chloe was able to clean more than 37 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.

  • Aπ‘₯>37
  • Bπ‘₯<37
  • Cπ‘₯<47
  • Dπ‘₯>47
  • Eπ‘₯β‰₯47

Q3:

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

  • A𝑐≀3
  • B𝑐>3
  • C𝑐<3
  • D𝑐β‰₯3

Q4:

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

  • Aπ‘₯>74
  • Bπ‘₯≀74
  • Cπ‘₯<74
  • Dπ‘₯β‰₯74

Q5:

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

  • Aπ‘₯β‰₯7,400
  • Bπ‘₯≀7,400
  • Cπ‘₯<7,400
  • Dπ‘₯>7,400

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.

  • A𝑑β‰₯9
  • B𝑑<9
  • C𝑑<7
  • D𝑑>7
  • E𝑑>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.

  • A𝑐>100
  • B𝑐≀100
  • C𝑐>101
  • D𝑐<100
  • E𝑐≀101

Q8:

A field 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.

  • A𝑆>40
  • B𝑆<40
  • C𝑆β‰₯40
  • D𝑆≀40
  • E𝑆β‰₯41

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.

  • Aπ‘Ž>5
  • Bπ‘Žβ‰₯6
  • Cπ‘Žβ‰€5
  • Dπ‘Žβ‰€4
  • Eπ‘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.

  • A𝑛≀4
  • B𝑛≀3
  • C𝑛>3
  • D𝑛<4
  • E𝑛β‰₯4

Q11:

Which of the following is an inequality?

  • A2π‘₯βˆ’7≀5
  • B12𝑛+4
  • C7βˆ’2(π‘₯βˆ’1)=4

Q12:

Rewrite the statement β€œπ‘¦ is between 8 and 10” using <, ≀, >, or β‰₯.

  • A8<𝑦>10
  • B10<𝑦≀8
  • C8>𝑦<10
  • D8≀𝑦≀10
  • E8<𝑦<10

Q13:

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

  • Aπ‘₯β‰₯0
  • Bπ‘₯β‰€βˆ’9
  • Cπ‘₯=0
  • Dπ‘₯>23

Q14:

Amelia 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.

  • A𝑑≀43
  • B𝑑<43
  • C𝑑≀35
  • D𝑑β‰₯43

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

  • ABetween 14:04 and 14:16
  • BAfter 14:04
  • CBefore 14:04
  • DAfter 14:16
  • EAt 14:16

Q15:

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

  • A𝑐≀5
  • B𝑐>5
  • C𝑐<5
  • D𝑐β‰₯5

Q16:

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

  • A𝑐≀1
  • B𝑐>1
  • C𝑐<1
  • D𝑐β‰₯1

Q17:

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

  • Aπ‘šβ‰€2
  • Bπ‘š>2
  • Cπ‘š<2
  • Dπ‘šβ‰₯2

Q18:

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

  • A𝑏≀4
  • B𝑏>4
  • C𝑏<4
  • D𝑏β‰₯4

Q19:

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

  • A𝑦≀6
  • B𝑦>6
  • C𝑦<6
  • D𝑦β‰₯6

Q20:

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

  • A𝑛≀7
  • B𝑛>7
  • C𝑛<7
  • D𝑛β‰₯7

Q21:

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

  • A𝑛≀8
  • B𝑛>8
  • C𝑛<8
  • D𝑛β‰₯8

Q22:

Given that π‘₯∈[βˆ’35,∞), which of the following inequalities holds?

  • Aπ‘₯>βˆ’35
  • Bπ‘₯β‰₯βˆ’35
  • Cπ‘₯<βˆ’35
  • Dπ‘₯β‰€βˆ’35

Q23:

What is the name of the set of all values that satisfy a given equation or inequality?

  • Athe solving set
  • Bthe substitution set
  • Cthe solution set
  • Dthe data set
  • Ethe satisfaction set

Q24:

Complete using <, =, or >: if 𝐴>𝐡, then π΄βˆ’πΆπ΅βˆ’πΆ.

  • A=
  • B<
  • C>

Q25:

Complete using <, =, or >: if 𝐴<𝐡, 𝐢<0, then 𝐴𝐢𝐡𝐢.

  • A=
  • B<
  • C>

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