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

Lesson: Inequalities and Interval Notation

Sample Question Videos

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 ]
Preview