Worksheet: Compound Linear Inequalities

In this worksheet, we will practice solving compound linear inequalities by applying inverse operations.

Q1:

Find all values of 𝑥 that satisfy 2 0 𝑥 3 𝑥 + 2 < 1 8 2 𝑥 . Write your answer as an interval.

  • A 1 1 2 , 4
  • B 1 1 2 , 1 6 5
  • C 9 2 , 4
  • D 1 1 2 , 1 6 5
  • E 1 1 2 , 1 6 5

Q2:

This number line describes the solution set to which of the following inequalities?

  • A 8 + 𝑥 7 𝑥 + 4 < 1 6 + 𝑥
  • B 8 + 𝑥 < 7 𝑥 + 4 1 6 + 𝑥
  • C 8 + 𝑥 7 𝑥 4 1 6 + 𝑥
  • D 8 + 𝑥 7 𝑥 + 4 1 6 + 𝑥
  • E 8 + 𝑥 7 𝑥 + 4 1 6 + 𝑥

Q3:

Which of the following is the set 𝐴 of all whole numbers 𝑥 such that 𝑥 + 3 < 6 ?

  • A 𝐴 = { 1 , 2 , 3 }
  • B 𝐴 = { 0 , 1 , 2 , 3 }
  • C 𝐴 = { 0 , 1 , 3 }
  • D 𝐴 = { 0 , 1 , 2 }

Q4:

Solve 5 3 𝑥 4 and 𝑥 + 3 < 5 .

  • A 𝑥 3
  • B 𝑥 3
  • C 𝑥 > 8
  • D 𝑥 < 8
  • E no solution

Q5:

Find the solution set of 1 2 < 𝑥 1 2 . Write your answer as an interval.

  • A ] 1 2 , 1 2 [
  • B ] 1 2 , 1 2 ]
  • C ] 1 2 , 1 2 ]
  • D [ 1 2 , 1 2 [
  • E { 1 2 , 1 2 }

Q6:

Find the solution set of 6 > 2 𝑥 + 1 0 > 1 6 , where 𝑥 .

  • A { 2 5 , 2 4 , , 1 7 }
  • B { 1 3 , 1 2 , , 8 }
  • C { 2 6 , 2 5 , , 1 6 }
  • D

Q7:

Find the solution set of 5 2 𝑥 + 3 7 given that 𝑥 .

  • A
  • B { 2 }
  • C { 1 }
  • D { 1 , 2 }

Q8:

Solve 1 0 𝑥 + 1 < 𝑥 8 and 𝑥 1 > 5 .

  • A 𝑥 > 4
  • B 𝑥 < 1
  • C 4 > 𝑥 > 1
  • D 4 < 𝑥 < 1
  • E 𝑥 > 3

Q9:

Find the solution set of 7 < 𝑥 1 2 < 1 1 , where 𝑥 .

  • A { 1 9 , 2 0 , 2 1 , 2 2 , 2 3 }
  • B { 2 0 , 2 1 , 2 2 , 2 3 }
  • C { 1 9 , 2 0 , 2 1 , 2 2 }
  • D { 2 0 , 2 1 , 2 2 }

Q10:

Given that 𝑧 , solve the inequality 5 6 𝑧 + 1 4 .

  • A 𝑧 𝑧 , 5 6 𝑧 2 3
  • B 𝑧 𝑧 , 1 𝑧 5 6
  • C 𝑧 𝑧 , 2 3 > 𝑧 > 1 2
  • D 𝑧 𝑧 , 2 3 𝑧 1 2
  • E 𝑧 𝑧 , 1 > 𝑧 > 5 6

Q11:

Find the solution set of the inequality in . Give your answer in interval notation.

  • A
  • B
  • C
  • D

Q12:

Find the solution set of the inequality | 1 | < 3 𝑥 8 7 in . Give your answer in interval notation.

  • A { 3 , 5 }
  • B [ 3 , 5 [
  • C [ 2 , 5 ]
  • D ] 3 , 5 ]
  • E ] 2 , 5 [

Q13:

Find the solution set of the inequality 4 > 3 𝑥 + 5 > 2 in . Give your answer in interval notation.

  • A 1 3 , 1
  • B 1 3 , 1
  • C 1 3 , 1
  • D 1 3 , 1
  • E 3 , 7 3

Q14:

Find the solution set of the inequality 2 3 𝑥 + 1 < 3 in . Give your answer in interval notation.

  • A 1 3 , 2 3
  • B 1 3 , 2 3
  • C 1 , 4 3
  • D 1 3 , 2 3
  • E 1 , 4 3

Q15:

Find the solution set of the inequality 4 < 5 𝑥 5 5 in . Give your answer in interval notation.

  • A 1 5 , 2
  • B 1 5 , 2
  • C 1 5 , 2
  • D 1 5 , 2
  • E 9 5 , 0

Q16:

Find the solution set of the inequality in . Give your answer in interval notation.

  • A
  • B
  • C
  • D

Q17:

Find the solution set of the inequality 3 < 𝑥 1 2 in . Give your answer in interval notation.

  • A { 3 , 1 2 }
  • B [ 3 , 1 2 ]
  • C [ 3 , 1 2 [
  • D ] 3 , 1 2 ]

Q18:

If 9 𝑥 < 5 , where 𝑥 , then what interval does 1 0 𝑥 lie in?

  • A { 9 0 , 5 0 }
  • B ] 9 0 , 5 0 ]
  • C [ 9 , 5 [
  • D [ 9 0 , 5 0 [
  • E { 9 , 5 }

Q19:

How many integer solutions does the inequality 1 2 < 𝑥 < 3 4 have?

  • A2
  • Binfinite
  • C3
  • D0

Q20:

Find the solution set of the inequality 3 6 4 𝑥 9 8 1 in . Give your answer in interval notation.

  • A [ 5 , 0 ]
  • B ] 1 3 , 1 8 ]
  • C [ 5 , 0 [
  • D [ 1 3 , 1 8 ]

Q21:

The solution set of 𝑎 𝑥 + 4 < 𝑏 is [ 6 , 1 0 [ . What are the values of 𝑎 and 𝑏 ?

  • A 𝑎 = 2 , 𝑏 = 6
  • B 𝑎 = 1 4 , 𝑏 = 1 0
  • C 𝑎 = 2 , 𝑏 = 1 4
  • D 𝑎 = 1 0 , 𝑏 = 1 4
  • E 𝑎 = 1 0 , 𝑏 = 6

Q22:

Solve 3 𝑥 5 < 4 and 𝑥 1 < 5 .

  • A 𝑥 = 3
  • B 𝑥 > 3
  • C 𝑥 < 3
  • D 𝑥 > 4
  • E 𝑥 < 4

Q23:

Fill in the blank in the following rule on inequalities: If 𝑦 > 𝑛 and 𝑛 > 𝑐 , then 𝑦 .

  • A = 𝑐
  • B < 𝑐
  • C 𝑐
  • D > 𝑐
  • E 𝑐

Q24:

Which of the following diagrams represents the solution set of the inequalities 3 𝑥 2 < 1 0 and 𝑥 + 2 > 3 ?

  • A
  • B
  • C
  • D

Q25:

Find all values of 𝑥 that satisfy 3 + 3 𝑥 7 𝑥 3 5 + 2 𝑥 . Write your answer as an interval.

  • A 3 2 , 8 5
  • B 3 2 , 8 5
  • C 3 2 , 8 5
  • D 3 2 , 8 5
  • E 3 2 , 8 5

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