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Worksheet: Solving Compound Linear Inequalities

Q1:

Find all values of that satisfy . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q2:

Find all values of that satisfy . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q3:

Find all values of that satisfy . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q4:

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

  • A βˆ’ 8 + π‘₯ ≀ 7 π‘₯ + 4 < 1 6 + π‘₯
  • B βˆ’ 8 + π‘₯ < 7 π‘₯ + 4 ≀ 1 6 + π‘₯
  • C βˆ’ 8 + π‘₯ ≀ 7 π‘₯ βˆ’ 4 ≀ 1 6 + π‘₯
  • D βˆ’ 8 + π‘₯ ≀ 7 π‘₯ + 4 ≀ 1 6 + π‘₯
  • E βˆ’ 8 + π‘₯ ≀ βˆ’ 7 π‘₯ + 4 ≀ 1 6 + π‘₯

Q5:

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

  • A βˆ’ 1 1 + π‘₯ < 2 π‘₯ βˆ’ 7 < βˆ’ 8 + π‘₯
  • B βˆ’ 1 1 + π‘₯ ≀ 2 π‘₯ βˆ’ 7 ≀ βˆ’ 8 + π‘₯
  • C βˆ’ 1 1 + π‘₯ < 2 π‘₯ + 7 ≀ βˆ’ 8 + π‘₯
  • D βˆ’ 1 1 + π‘₯ < 2 π‘₯ βˆ’ 7 ≀ βˆ’ 8 + π‘₯
  • E βˆ’ 1 1 + π‘₯ < βˆ’ 2 π‘₯ βˆ’ 7 ≀ βˆ’ 8 + π‘₯

Q6:

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

  • A βˆ’ 4 + π‘₯ < 2 π‘₯ βˆ’ 5 < 1 + π‘₯
  • B βˆ’ 4 + π‘₯ ≀ 2 π‘₯ βˆ’ 5 ≀ 1 + π‘₯
  • C βˆ’ 4 + π‘₯ < 2 π‘₯ + 5 ≀ 1 + π‘₯
  • D βˆ’ 4 + π‘₯ < 2 π‘₯ βˆ’ 5 ≀ 1 + π‘₯
  • E βˆ’ 4 + π‘₯ < βˆ’ 2 π‘₯ βˆ’ 5 ≀ 1 + π‘₯

Q7:

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

  • A βˆ’ 7 + π‘₯ ≀ 2 π‘₯ βˆ’ 4 ≀ βˆ’ 3 + π‘₯
  • B βˆ’ 7 + π‘₯ < 2 π‘₯ βˆ’ 4 < βˆ’ 3 + π‘₯
  • C βˆ’ 7 + π‘₯ ≀ 2 π‘₯ + 4 < βˆ’ 3 + π‘₯
  • D βˆ’ 7 + π‘₯ ≀ 2 π‘₯ βˆ’ 4 < βˆ’ 3 + π‘₯
  • E βˆ’ 7 + π‘₯ ≀ βˆ’ 2 π‘₯ βˆ’ 4 < βˆ’ 3 + π‘₯

Q8:

Which of the following is the set 𝐴 of all whole numbers π‘₯ such that π‘₯ + 3 < 6 ?

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

Q9:

Solve βˆ’ 5 βˆ’ 3 π‘₯ β‰₯ 4 and π‘₯ + 3 < βˆ’ 5 .

  • A π‘₯ β‰₯ βˆ’ 3
  • B π‘₯ ≀ βˆ’ 3
  • C π‘₯ > βˆ’ 8
  • D π‘₯ < βˆ’ 8
  • E no solution

Q10:

Find the solution set of . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q11:

Find the solution set of βˆ’ 6 > 2 π‘₯ + 1 0 > βˆ’ 1 6 , where π‘₯ ∈ β„• .

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

Q12:

Find the solution set of 5 ≀ 2 π‘₯ + 3 ≀ 7 given that π‘₯ ∈ β„• .

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

Q13:

Solve 1 0 π‘₯ + 1 < π‘₯ βˆ’ 8 and π‘₯ βˆ’ 1 > βˆ’ 5 .

  • A π‘₯ > βˆ’ 4
  • B π‘₯ < βˆ’ 1
  • C βˆ’ 4 > π‘₯ > βˆ’ 1
  • D βˆ’ 4 < π‘₯ < βˆ’ 1
  • E π‘₯ > βˆ’ 3

Q14:

Find the solution set of 7 < π‘₯ βˆ’ 1 2 < 1 1 , where π‘₯ ∈ β„• .

  • 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 }

Q15:

Given that 𝑧 ∈ β„š , solve the inequality 5 β‰₯ 6 𝑧 + 1 β‰₯ 4 .

  • A  𝑧 ∢ 𝑧 ∈ β„š , 5 6 β‰₯ 𝑧 β‰₯ 2 3 
  • B  𝑧 ∢ 𝑧 ∈ β„š , 1 β‰₯ 𝑧 β‰₯ 5 6 
  • C  𝑧 ∢ 𝑧 ∈ β„š , 2 3 > 𝑧 > 1 2 
  • D  𝑧 ∢ 𝑧 ∈ β„š , 2 3 β‰₯ 𝑧 β‰₯ 1 2 
  • E  𝑧 ∢ 𝑧 ∈ β„š , 1 > 𝑧 > 5 6 

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 in . Give your answer in interval notation.

  • A
  • B
  • C
  • D
  • E

Q18:

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

  • A
  • B
  • C
  • D
  • E

Q19:

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

  • A
  • B
  • C
  • D
  • E

Q20:

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

  • A
  • B
  • C
  • D
  • E

Q21:

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

  • A
  • B
  • C
  • D

Q22:

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

  • A
  • B
  • C
  • D

Q23:

If , where , then what interval does lie in?

  • A
  • B
  • C
  • D
  • E

Q24:

How many integer solutions does the inequality 1 2 < π‘₯ < 3 4 have?

  • A2
  • Binfinite
  • C3
  • D0

Q25:

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

  • A
  • B
  • C
  • D