Worksheet: Inequalities and Interval Notation

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

Q1:

Find all values of 𝑥 that satisfy 18𝑥+41. 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 24𝑥14 in . Give your answer in interval notation.

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

Q3:

Find the solution set of the inequality 2𝑥+623 in . Give your answer in interval notation.

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

Q4:

Find the solution set of the inequality 𝑥20 in . Give your answer in interval notation.

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

Q5:

Find the solution set of the inequality 4𝑥1<5 in . Give your answer in interval notation.

  • A 3 2 ,
  • B 3 2 ,
  • C , 3 2
  • D ( 1 , )

Q6:

Find the solution set of the inequality 𝑥+25 in . Give your answer in interval notation.

  • A [ 3 , )
  • B [ 7 , )
  • C ( 3 , )
  • D [ 3 , ]
  • E ( 3 , ]

Q7:

Find the solution set of the inequality 13𝑥+4>4 in . Give your answer in interval notation.

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

Q8:

Find the solution set of the inequality 2<4𝑥3<2 in . Give your answer in interval notation.

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

Q9:

Find the solution set of the inequality 515𝑥2<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 )

Q10:

Find the solution set of the inequality 5𝑥110<2𝑥+5<𝑥+32 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

Q11:

If 6<𝑥4, then what interval does 3𝑥5 lie in?

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

Q12:

Find the solution set of the inequality 22𝑥42 in . Give your answer in interval notation.

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

Q13:

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

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

Q14:

Find the solution set of the inequality 014𝑥+13 in . Give your answer in interval notation.

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

Q15:

Find all values of 𝑥 that satisfy 20𝑥3𝑥+2<182𝑥. Write your answer as an interval.

  • A 1 1 2 , 1 6 5
  • B 9 2 , 4
  • C 1 1 2 , 4
  • D 1 1 2 , 1 6 5
  • E 1 1 2 , 1 6 5

Q16:

Find the solution set of 12<𝑥12. Write your answer as an interval.

  • A [ 1 2 , 1 2 )
  • B ( 1 2 , 1 2 )
  • C ( 1 2 , 1 2 ]
  • D { 1 2 , 1 2 }
  • E ( 1 2 , 1 2 ]

Q17:

Find the solution set of the inequality 48𝑥<2 in . Give your answer in interval notation.

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

Q18:

Find the solution set of the inequality |1|<3𝑥87 in . Give your answer in interval notation.

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

Q19:

Find the solution set of the inequality 4>3𝑥+5>2 in . Give your answer in interval notation.

  • A 1 3 , 1
  • B 1 3 , 1
  • C 1 3 , 1
  • D 1 3 , 1
  • E 3 , 7 3

Q20:

Find the solution set of the inequality 23𝑥+1<3 in . Give your answer in interval notation.

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

Q21:

Find the solution set of the inequality 4<5𝑥55 in . Give your answer in interval notation.

  • A 1 5 , 2
  • B 1 5 , 2
  • C 1 5 , 2
  • D 1 5 , 2
  • E 9 5 , 0

Q22:

Find the solution set of the inequality 17<𝑥<32 in . Give your answer in interval notation.

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

Q23:

Find the solution set of the inequality 3<𝑥12 in . Give your answer in interval notation.

  • A { 3 , 1 2 }
  • B ( 3 , 1 2 ]
  • C [ 3 , 1 2 ]
  • D [ 3 , 1 2 )

Q24:

If 9𝑥<5, where 𝑥, then what interval does 10𝑥 lie in?

  • A [ 9 0 , 5 0 )
  • B { 9 , 5 }
  • C { 9 0 , 5 0 }
  • D ( 9 0 , 5 0 ]
  • E [ 9 , 5 )

Q25:

Find all the values of 𝑥 that satisfy 11<7𝑥+432. Give your answer in interval form.

  • A ( 7 , 2 8 ]
  • B ( 1 , 4 ]
  • C [ 1 , 4 ]
  • D ( 1 , 4 )
  • E [ 7 , 2 8 ]

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