Worksheet: Inequalities with Variables on Both Sides

In this worksheet, we will learn how to solve multistep linear inequalities including those involving the distributive property.

Q1:

What inequality involving 𝑥 is equivalent to the inequality 1 3 𝑥 4 < 5 𝑥 + 2 ?

  • A 𝑥 < 9 7
  • B 𝑥 > 9 8
  • C 𝑥 > 1 1 4
  • D 𝑥 > 9 7
  • E 𝑥 > 9 7

Q2:

Solve the inequality 2 6 ( 9 𝑑 2 ) > 7 ( 𝑑 5 ) in .

  • A 𝑑 𝑑 , 𝑑 > 6 3 1 6
  • B 𝑑 𝑑 , 𝑑 > 5 9 2
  • C 𝑑 𝑑 , 𝑑 < 6 3 1 6
  • D 𝑑 𝑑 , 𝑑 < 3 3 1 6
  • E 𝑑 𝑑 , 𝑑 > 7 1 6

Q3:

Solve the inequality 8 + 5 ( 𝑥 1 ) 3 ( 9 + 9 𝑥 ) in .

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

Q4:

This number line describes the solution set to which of the following inequalities?

  • A 8 𝑥 + 1 6 1 6 𝑥
  • B 8 𝑥 1 6 1 6 𝑥
  • C 8 𝑥 + 1 6 1 6 𝑥
  • D 8 𝑥 1 6 < 1 6 𝑥
  • E 8 𝑥 + 1 6 < 1 6 𝑥

Q5:

Solve the following inequality: 9 𝑦 > 7 7 + 2 𝑦 .

  • A 𝑦 < 1 1
  • B 𝑦 > 7 7
  • C 𝑦 > 7
  • D 𝑦 > 1 1
  • E 𝑦 < 7

Q6:

Solve the inequality 9 7 𝑦 8 9 2 𝑦 + 4 0 in .

  • A 𝑦 𝑦 , 𝑦 3 2 6 1
  • B 𝑦 𝑦 , 𝑦 3 2 6 5
  • C 𝑦 𝑦 , 𝑦 4 8 6 1
  • D 𝑦 𝑦 , 𝑦 4 8 6 5
  • E 𝑦 𝑦 , 𝑦 4 8 6 5

Q7:

Solve the following inequality: 9 𝑥 + 1 4 2 0 8 𝑥 .

  • A 𝑥 3 4
  • B 𝑥 2
  • C 𝑥 3 4
  • D 𝑥 3 4
  • E 𝑥 3 4

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