Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Compound Linear Inequalities

Video

15:53

Sample Question Videos

Worksheet • 25 Questions • 1 Video

Q1:

Find all values of π‘₯ that satisfy βˆ’ 2 0 βˆ’ π‘₯ ≀ 3 π‘₯ + 2 < 1 8 βˆ’ 2 π‘₯ . Write your answer as an interval.

  • A  βˆ’ 1 1 2 , 1 6 5 
  • B  βˆ’ 1 1 2 , 1 6 5 
  • C  βˆ’ 1 1 2 , 1 6 5 
  • D  βˆ’ 9 2 , 4 
  • E  βˆ’ 1 1 2 , 4 

Q2:

Find all values of π‘₯ that satisfy 3 + 3 π‘₯ ≀ 7 π‘₯ βˆ’ 3 ≀ 5 + 2 π‘₯ . 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 

Q3:

Find all values of π‘₯ that satisfy βˆ’ 1 1 βˆ’ π‘₯ < 6 π‘₯ βˆ’ 3 ≀ βˆ’ 3 βˆ’ π‘₯ . Write your answer as an interval.

  • A  βˆ’ 8 7 , 0 
  • B  βˆ’ 8 7 , 0 
  • C  βˆ’ 8 7 , 0 
  • D  βˆ’ 2 , βˆ’ 6 7 
  • E  βˆ’ 8 7 , βˆ’ 6 7 

Q4:

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

  • A
  • B
  • C
  • D

Q5:

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

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

Q6:

Find the solution set of the inequality | βˆ’ 1 | < 3 π‘₯ βˆ’ 8 ≀ 7 in ℝ . Give your answer in interval notation.

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

Q7:

Find the solution set of βˆ’ 1 2 < βˆ’ π‘₯ ≀ 1 2 . Write your answer as an interval.

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

Q8:

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

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

Q9:

Find the solution set of the inequality 4 > βˆ’ 3 π‘₯ + 5 > 2 in ℝ . Give your answer in interval notation.

  • A  1 3 , 1 
  • B  βˆ’ 3 , βˆ’ 7 3 
  • C  1 3 , 1 
  • D  1 3 , 1 
  • E  1 3 , 1 

Q10:

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

  • A0
  • Binfinite
  • C3
  • D2

Q11:

Find the solution set of the inequality 2 ≀ 3 π‘₯ + 1 < 3 in ℝ . Give your answer in interval notation.

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

Q12:

Find the solution set of the inequality 3 √ 6 4 ≀ π‘₯ βˆ’ 9 ≀ √ 8 1 in ℝ . Give your answer in interval notation.

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

Q13:

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

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

Q14:

Find the solution set of the inequality βˆ’ 4 < 5 π‘₯ βˆ’ 5 ≀ 5 in ℝ . Give your answer in interval notation.

  • A  1 5 , 2 
  • B  βˆ’ 9 5 , 0 
  • C  1 5 , 2 
  • D  1 5 , 2 
  • E  1 5 , 2 

Q15:

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

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

Q16:

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

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

Q17:

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

Q18:

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

Q19:

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

Q20:

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

Q21:

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

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

Q22:

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

  • A
  • B
  • C
  • D

Q23:

Find the solution set of the inequality βˆ’ 3 < π‘₯ ≀ 1 2 in ℝ . Give your answer in interval notation.

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

Q24:

If βˆ’ 9 ≀ π‘₯ < 5 , where π‘₯ ∈ ℝ , then what interval does 1 0 π‘₯ lie in?

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

Q25:

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

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