Worksheet: Inequalities and Interval Notation

In this worksheet, we will practice solving simple and compound linear inequalities and expressing their solution sets using interval notation.

Q1:

Find all values of 𝑥 that satisfy 1 8 𝑥 + 4 1 . Write your answer as an interval.

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

Q2:

Find the solution set of the inequality 4 𝑥 + 4 2 in .

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

Q3:

Find the solution set of the inequality 2 4 𝑥 1 4 in . Give your answer in interval notation.

  • A 1 4 , 5 4
  • B 1 4 , 5 4
  • C 1 4 , 5 4
  • D 1 4 , 5 4
  • E 3 4 , 3 4

Q4:

Find the solution set of the inequality 2 𝑥 + 6 2 3 in . 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 𝑥 2 0 in . Give your answer in interval notation.

  • A ( 2 0 , )
  • B ( 2 0 , )
  • C ( , 2 0 )
  • D ( , 2 0 ]

Q6:

Find the solution set of the inequality 4 𝑥 1 < 5 in . Give your answer in interval notation.

  • A , 3 2
  • B 3 2 ,
  • C ( 1 , )
  • D 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 3 𝑥 + 4 > 4 in . Give your answer in interval notation.

  • A 8 3 , 1
  • B 8 3 , 1
  • C 8 3 , 1
  • D 8 3 , 1
  • E 0 , 5 3

Q9:

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

  • A 1 4 , 5 4
  • B 1 4 , 5 4
  • C 1 4 , 5 4
  • D 1 4 , 5 4
  • E 5 4 , 1 4

Q10:

Find the solution set of the inequality 2 4 𝑥 + 5 5 in .

  • A 5 2 , 7 4
  • B 5 2 , 7 4
  • C 5 2 , 7 4
  • D 5 2 , 7 4
  • E 0 , 3 4

Q11:

Find the solution set of the inequality 5 > 𝑥 1 4 in .

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

Q12:

Find the solution set of the inequality 5 1 5 𝑥 2 < 2 in . Give your answer in interval notation.

  • A [ 1 5 , 2 0 ]
  • B ( 1 5 , 2 0 ]
  • C ( 1 5 , 2 0 )
  • D [ 1 5 , 2 0 )

Q13:

Find the solution set of the inequality 5 𝑥 1 1 0 < 2 𝑥 + 5 < 𝑥 + 3 2 in . 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 6 < 𝑥 4 , then what interval does 3 𝑥 5 lie in?

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

Q15:

Find the solution set of 𝑥 + 1 | 5 | given that 𝑥 .

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

Q16:

Find the solution set of the inequality 3 𝑥 2 1 in .

  • A ( 1 , ]
  • B [ 1 , ]
  • C ( 1 , )
  • D [ 1 , )
  • E 1 3 ,

Q17:

Find the solution set of the inequality 4 𝑥 5 4 in .

  • A 1 4 ,
  • B 1 4 ,
  • C 1 4 ,
  • D 1 4 ,
  • E 9 4 ,

Q18:

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

  • A ( 3 , 1 )
  • B ( 3 , 1 ]
  • C { 3 , 1 }
  • D [ 3 , 1 ]
  • E [ 1 , 3 ]

Q19:

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

  • A 7 5 , 1 5
  • B 7 5 , 1 5
  • C 7 5 , 1 5
  • D 7 5 , 1 5
  • E 1 5 , 7 5

Q20:

Find the solution set of the inequality 0 1 4 𝑥 + 1 3 in . Give your answer in interval notation.

  • A ( 4 , 8 ]
  • B ( 4 , 8 )
  • C [ 4 , 8 )
  • D [ 4 , 8 ]

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