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Lesson: Inequalities and Interval Notation

In this lesson, we will learn how to solve simple and compound linear inequalities and how to express their solution sets using interval notation.

Sample Question Videos

03:17

Worksheet • 20 Questions • 1 Video

Q1:

Find all values of π‘₯ that satisfy βˆ’ 1 8 ≀ βˆ’ π‘₯ + 4 ≀ βˆ’ 1 . Write your answer as an interval.

  • A [ 5 , 2 2 ]
  • B ] 5 , 2 2 ]
  • C ] βˆ’ 3 , 1 4 ]
  • D [ βˆ’ 3 , 1 4 ]

Q2:

Find the solution set of the inequality 4 π‘₯ + 4 β‰₯ βˆ’ 2 in ℝ .

  • A  βˆ’ 3 2 , ∞ 
  • B  1 2 , ∞ 
  • C  βˆ’ 3 2 , ∞ 
  • D  βˆ’ 3 2 , ∞ 
  • E  βˆ’ 3 2 , ∞ 

Q3:

Find the solution set of the inequality βˆ’ 2 ≀ 4 π‘₯ βˆ’ 1 ≀ 4 in ℝ . Give your answer in interval notation.

  • A  βˆ’ 1 4 , 5 4 
  • B  βˆ’ 3 4 , 3 4 
  • C  βˆ’ 1 4 , 5 4 
  • D  βˆ’ 1 4 , 5 4 
  • E  βˆ’ 1 4 , 5 4 

Q4:

Find the solution set of the inequality 2 ≀ βˆ’ π‘₯ + 6 2 ≀ 3 in ℝ . Give your answer in interval notation.

  • A [ 0 , 2 ]
  • B ] 0 , 2 [
  • C ] 0 , 2 ]
  • D { 0 , 2 }
  • E [ 0 , 2 [

Q5:

Find the solution set of the inequality π‘₯ ≀ 2 0 in ℝ . Give your answer in interval notation.

  • A ] βˆ’ ∞ , 2 0 ]
  • B ] βˆ’ 2 0 , ∞ [
  • C ] βˆ’ ∞ , 2 0 [
  • D ] 2 0 , ∞ [

Q6:

Find the solution set of the inequality βˆ’ 4 π‘₯ βˆ’ 1 < 5 in ℝ . Give your answer in interval notation.

  • A  βˆ’ 3 2 , ∞ 
  • B  βˆ’ 3 2 , ∞ 
  • C ] βˆ’ 1 , ∞ [
  • D  βˆ’ ∞ , βˆ’ 3 2 

Q7:

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

  • A
  • B
  • C
  • D
  • E

Q8:

Find the solution set of the inequality 1 β‰₯ 3 π‘₯ + 4 > βˆ’ 4 in ℝ . Give your answer in interval notation.

  • A  βˆ’ 8 3 , βˆ’ 1 
  • B  0 , 5 3 
  • C  βˆ’ 8 3 , βˆ’ 1 
  • D  βˆ’ 8 3 , βˆ’ 1 
  • E  βˆ’ 8 3 , βˆ’ 1 

Q9:

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

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

Q10:

Find the solution set of the inequality βˆ’ 2 β‰₯ 4 π‘₯ + 5 β‰₯ βˆ’ 5 in ℝ .

  • A  βˆ’ 5 2 , βˆ’ 7 4 
  • B  0 , 3 4 
  • C  βˆ’ 5 2 , βˆ’ 7 4 
  • D  βˆ’ 5 2 , βˆ’ 7 4 
  • E  βˆ’ 5 2 , βˆ’ 7 4 

Q11:

Find the solution set of the inequality 5 > π‘₯ βˆ’ 1 β‰₯ 4 in ℝ .

  • A [ 5 , 6 [
  • B [ 3 , 4 [
  • C ] 5 , 6 [
  • D { 5 , 6 }
  • E [ 5 , 6 ]

Q12:

Find the solution set of the inequality βˆ’ 5 ≀ 1 5 π‘₯ βˆ’ 2 < 2 in ℝ . Give your answer in interval notation.

  • A [ βˆ’ 1 5 , 2 0 [
  • B ] βˆ’ 1 5 , 2 0 ]
  • C ] βˆ’ 1 5 , 2 0 [
  • D [ βˆ’ 1 5 , 2 0 ]

Q13:

Find the solution set of the inequality 5 π‘₯ βˆ’ 1 1 0 < βˆ’ 2 π‘₯ + 5 < π‘₯ + 3 2 in ℝ . Give your answer in interval notation.

  • A  7 5 , 5 1 2 5 
  • B  7 5 , 5 1 2 5 
  • C  7 5 , 5 1 2 5 
  • D  7 5 , 5 1 2 5 
  • E  7 5 , 5 1 2 5 

Q14:

If βˆ’ 6 < π‘₯ ≀ 4 , then what interval does 3 π‘₯ βˆ’ 5 lie in?

  • A ( βˆ’ 2 3 , 7 ]
  • B [ βˆ’ 2 3 , 7 )
  • C ( βˆ’ 1 8 , βˆ’ 2 0 ]
  • D ( βˆ’ 1 1 , βˆ’ 1 ]

Q15:

Find the solution set of π‘₯ + 1 β‰₯ | βˆ’ 5 | given that π‘₯ ∈ β„• .

  • A { 4 , 5 , 6 , … }
  • B { βˆ’ 1 , 0 , 1 , 2 , 3 }
  • C { 5 , 6 , 7 , … }
  • D { 1 , 2 , 3 , 4 }

Q16:

Find the solution set of the inequality 3 π‘₯ βˆ’ 2 β‰₯ 1 in ℝ .

  • A [ 1 , ∞ [
  • B  βˆ’ 1 3 , ∞ 
  • C [ 1 , ∞ ]
  • D ] 1 , ∞ [
  • E ] 1 , ∞ ]

Q17:

Find the solution set of the inequality 4 π‘₯ βˆ’ 5 β‰₯ βˆ’ 4 in ℝ .

  • A  1 4 , ∞ 
  • B  βˆ’ 9 4 , ∞ 
  • C  1 4 , ∞ 
  • D  1 4 , ∞ 
  • E  1 4 , ∞ 

Q18:

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

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

Q19:

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

  • A  βˆ’ 7 5 , βˆ’ 1 5 
  • B  1 5 , 7 5 
  • C  βˆ’ 7 5 , βˆ’ 1 5 
  • D  βˆ’ 7 5 , βˆ’ 1 5 
  • E  βˆ’ 7 5 , βˆ’ 1 5 

Q20:

Find the solution set of the inequality 0 ≀ 1 4 π‘₯ + 1 ≀ 3 in ℝ . Give your answer in interval notation.

  • A [ βˆ’ 4 , 8 ]
  • B ] βˆ’ 4 , 8 [
  • C [ βˆ’ 4 , 8 [
  • D ] βˆ’ 4 , 8 ]
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