Worksheet: Multistep Inequalities

In this worksheet, we will practice solving multistep inequalities.

Q1:

Find all values of 𝑥 that satisfy 4 + 𝑥 < 2 𝑥 5 < 7 + 𝑥 . Write your answer as an interval.

  • A ] 9 , 1 2 ]
  • B [ 9 , 1 2 [
  • C [ 9 , 1 2 ]
  • D ] 9 , 1 2 [
  • E { 9 , 1 2 }

Q2:

Solve the inequality 5 1 2 𝑥 1 0 for 𝑥 .

  • A 𝑥 1 0
  • B 𝑥 1 0 3
  • C 𝑥 1 0
  • D 𝑥 1 0
  • E 𝑥 1 5

Q3:

Solve the following inequality: 𝑛 5 + 1 < 6 .

  • A 𝑛 > 2 5
  • B 𝑛 < 3 5
  • C 𝑛 > 3 5
  • D 𝑛 < 2 5
  • E 𝑛 > 1 2

Q4:

Write the set of all integer solutions to 4 𝑥 8 < 4 .

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

Q5:

Solve 5 𝑥 + 7 < 3 . Write your answer as an interval.

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

Q6:

Determine the solution set of given that .

  • A
  • B
  • C
  • D

Q7:

Given that 𝑥 , write the solution set of 2 𝑥 6 𝑥 1 .

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

Q8:

Find the solution set of the inequality 2 𝑥 + 3 5 . Write your answer as an interval.

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

Q9:

Solve the inequality 5 𝑚 9 ( 𝑚 + 3 ) < 1 4 in .

  • A 𝑚 𝑚 , 𝑚 > 1 3 4
  • B 𝑚 𝑚 , 𝑚 < 1 3 1 4
  • C 𝑚 𝑚 , 𝑚 > 4 1 1 4
  • D 𝑚 𝑚 , 𝑚 > 4 1 4
  • E 𝑚 𝑚 , 𝑚 > 1 3 1 4

Q10:

Find the solution set of the inequality 6 𝑥 1 7 < 5 𝑥 + 4 6 𝑥 3 in . Give your answer in interval notation.

  • A ] 2 1 , 7 [
  • B [ 2 1 , 7 [
  • C { 2 1 , 7 }
  • D ] 2 1 , 7 ]

Q11:

Find the solution set of the inequality 1 4 𝑥 5 2 1 8 𝑥 in . Give your answer in interval notation.

  • A ] , 1 3 [
  • B [ 1 3 , [
  • C ] , 1 3 ]
  • D ] , 1 3 ]

Q12:

Find the solution set of the inequality 3 𝑥 9 𝑥 1 2 + 3 𝑥 in . Give your answer in interval notation.

  • A { 1 , 0 }
  • B ] 1 , 0 [
  • C ] 1 , 0 ]
  • D [ 1 , 0 ]

Q13:

The solution set of the inequality 4 7 𝑥 1 0 7 4 is [ 𝑚 , 𝑚 + 𝑛 ] , where 𝑚 and 𝑛 are real numbers. What is the value of 𝑛 ?

Q14:

Solve the inequality 1 7 + 7 ( 𝑥 1 3 ) 𝑥 + 4 4 in .

  • A { 𝑥 𝑥 , 𝑥 8 }
  • B 𝑥 𝑥 , 𝑥 2 0 3
  • C { 𝑥 𝑥 , 𝑥 5 }
  • D 𝑥 𝑥 , 𝑥 5 9 3
  • E 𝑥 𝑥 , 𝑥 5 9 3

Q15:

Solve the inequality 7 𝑥 8 𝑥 + 1 1 8 in .

  • A 𝑥 𝑥 , 𝑥 1 5
  • B { 𝑥 𝑥 , 𝑥 1 9 }
  • C 𝑥 𝑥 , 𝑥 1 5
  • D { 𝑥 𝑥 , 𝑥 3 }
  • E { 𝑥 𝑥 , 𝑥 1 9 }

Q16:

Find the solution set of 2 𝑥 1 9 given that 𝑥 .

  • A { 4 }
  • B { 6 , 5 }
  • C { 6 , 5 }
  • D

Q17:

Solve the inequality 1 0 𝑥 + 1 6 8 ( 𝑥 1 9 ) in .

  • A { 𝑥 𝑥 , 𝑥 6 8 }
  • B 𝑥 𝑥 , 𝑥 3 5 9
  • C { 𝑥 𝑥 , 𝑥 8 4 }
  • D { 𝑥 𝑥 , 𝑥 8 4 }

Q18:

Solve the inequality 6 𝑥 2 7 4 4 5 in .

  • A 𝑥 𝑥 , 𝑥 1 5 1 3 0
  • B 𝑥 𝑥 , 𝑥 1 1 9 3 0
  • C 𝑥 𝑥 , 𝑥 1 5 1 3 0
  • D 𝑥 𝑥 , 𝑥 1 5 1 3 0
  • E 𝑥 𝑥 , 𝑥 1 1 9 3 0

Q19:

Given that 𝑧 , solve the inequality 4 ( 𝑧 3 ) ( 4 𝑧 4 ) 3 ( 3 𝑧 1 ) .

  • A 𝑧 𝑧 , 𝑧 2 3
  • B 𝑧 𝑧 , 𝑧 1 9 9
  • C 𝑧 𝑧 , 𝑧 < 1 3 9
  • D 𝑧 𝑧 , 𝑧 1 3 9
  • E 𝑧 𝑧 , 𝑧 2 3

Q20:

Solve the inequality 1 0 ( 𝑥 + 2 ) < 1 6 𝑥 2 2 in .

  • A 𝑥 𝑥 , 𝑥 > 1 2 1 3
  • B 𝑥 𝑥 , 𝑥 < 1 1 3
  • C 𝑥 𝑥 , 𝑥 > 2 1 1 3
  • D 𝑥 𝑥 , 𝑥 > 1 1 3

Q21:

Solve the inequality 4 ( 𝑦 + 4 ) 1 2 < 5 0 ( 4 7 𝑦 ) in .

  • A 𝑦 𝑦 , 𝑦 > 2 5 3
  • B { 𝑦 𝑦 , 𝑦 > 2 3 }
  • C 𝑦 𝑦 , 𝑦 > 8 9 5
  • D 𝑦 𝑦 , 𝑦 > 6 9 5
  • E 𝑦 𝑦 , 𝑦 < 6 9 5

Q22:

Solve the inequality 9 𝑥 3 ( 7 𝑥 + 9 ) < 7 ( 9 + 𝑥 ) 2 in .

  • A 𝑥 𝑥 , 𝑥 > 1 0 4 3 7
  • B 𝑥 𝑥 , 𝑥 < 1 0 4 3 7
  • C 𝑥 𝑥 , 𝑥 > 3 4 5
  • D 𝑥 𝑥 , 𝑥 < 8 8 3 7
  • E 𝑥 𝑥 , 𝑥 < 3 4 5

Q23:

Solve the inequality 𝑥 8 8 7 𝑥 2 9 in .

  • A 𝑥 𝑥 , 𝑥 2 9 6 5 7
  • B 𝑥 𝑥 , 𝑥 2 9 6 5 7
  • C 𝑥 𝑥 , 𝑥 1 6 8 5 5
  • D 𝑥 𝑥 , 𝑥 5 6 1 9
  • E 𝑥 𝑥 , 𝑥 1 6 8 5 5

Q24:

Solve the inequality 6 ( 𝑥 3 ) 4 ( 𝑥 + 5 ) in .

  • A 𝑥 𝑥 , 𝑥 1 9 5
  • B 𝑥 𝑥 , 𝑥 1 9 5
  • C 𝑥 𝑥 , 𝑥 1 5
  • D 𝑥 𝑥 , 𝑥 1 5
  • E 𝑥 𝑥 , 𝑥 1 9 5

Q25:

Find the solution set of the inequality 3 𝑥 + 1 1 𝑥 + 3 7 in . Give your answer in interval notation.

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

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