Worksheet: Multistep Inequalities

Start Practicing

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 ∈ ℤ , 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 ℚ .

  • A 𝑚 ∶ 𝑚 ∈ ℚ , 𝑚 > 1 3 4
  • B 𝑚 ∶ 𝑚 ∈ ℚ , 𝑚 < − 1 3 1 4
  • C 𝑚 ∶ 𝑚 ∈ ℚ , 𝑚 > − 4 1 1 4
  • D 𝑚 ∶ 𝑚 ∈ ℚ , 𝑚 > − 4 1 4
  • E 𝑚 ∶ 𝑚 ∈ ℚ , 𝑚 > − 1 3 1 4

Q10:

Find the solution set of the inequality − 6 𝑥 − 1 7 < − 5 𝑥 + 4 ≤ − 6 𝑥 − 3 in ℝ . 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 ℝ . 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 ℝ . 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 ℚ .

  • A { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 8 }
  • B 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ 2 0 3
  • C { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ 5 }
  • D 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ 5 9 3
  • E 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 5 9 3

Q15:

Solve the inequality 7 𝑥 − 8 𝑥 + 1 1 ≤ 8 in ℚ .

  • A 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 1 5
  • B { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ − 1 9 }
  • C 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ 1 5
  • D { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ 3 }
  • E { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 1 9 }

Q16:

Find the solution set of 2 𝑥 − 1 ≤ − 9 given that 𝑥 ∈ ℕ .

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

Q17:

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

  • A { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 6 8 }
  • B 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 3 5 9
  • C { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ − 8 4 }
  • D { 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 8 4 }

Q18:

Solve the inequality 6 𝑥 − 2 7 4 ≥ 4 5 in ℚ .

  • A 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 1 5 1 3 0
  • B 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ − 1 1 9 3 0
  • C 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 1 5 1 3 0
  • D 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ 1 5 1 3 0
  • E 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 1 1 9 3 0

Q19:

Given that 𝑧 ∈ ℚ , solve the inequality − 4 ( 𝑧 − 3 ) − ( − 4 𝑧 − 4 ) ≤ − 3 ( 3 𝑧 − 1 ) .

  • A 𝑧 ∶ 𝑧 ∈ ℚ , 𝑧 ≤ − 2 3
  • B 𝑧 ∶ 𝑧 ∈ ℚ , 𝑧 ≥ − 1 9 9
  • C 𝑧 ∶ 𝑧 ∈ ℚ , 𝑧 < − 1 3 9
  • D 𝑧 ∶ 𝑧 ∈ ℚ , 𝑧 ≤ − 1 3 9
  • E 𝑧 ∶ 𝑧 ∈ ℚ , 𝑧 ≥ − 2 3

Q20:

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

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

Q21:

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

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

Q22:

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

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

Q23:

Solve the inequality 𝑥 8 − 8 ≤ − 7 𝑥 − 2 9 in ℚ .

  • A 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ − 2 9 6 5 7
  • B 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 2 9 6 5 7
  • C 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ 1 6 8 5 5
  • D 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 5 6 1 9
  • E 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 1 6 8 5 5

Q24:

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

  • A 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ 1 9 5
  • B 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 1 9 5
  • C 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ − 1 5
  • D 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≤ − 1 5
  • E 𝑥 ∶ 𝑥 ∈ ℚ , 𝑥 ≥ − 1 9 5

Q25:

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

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

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