Worksheet: Solving Inequalities by Multiplication or Division

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In this worksheet, we will practice solving inequalities by multiplying both sides by a number.

Q1:

Solve 5 𝑥 > 4 5 for 𝑥 .

  • A 𝑥 = 9
  • B 𝑥 < 9
  • C 𝑥 > 4 0
  • D 𝑥 > 9
  • E 𝑥 = 4 0

Q2:

Solve the following inequality: 1 4 < 4 9 𝑦 .

  • A 1 9 < 𝑦
  • B 9 1 6 > 𝑦
  • C 1 9 > 𝑦
  • D 9 1 6 < 𝑦
  • E 1 6 9 < 𝑦

Q3:

If − 4 2 𝑥 < − 4 1 , then .

  • A 𝑥 < 4 1 4 2
  • B 𝑥 > − 4 1 4 2
  • C 𝑥 < − 4 1 4 2
  • D 𝑥 > 4 1 4 2

Q4:

Given that − 1 ≤ − 6 𝑥 1 0 − 1 ≤ 5 , find the greatest possible value of 𝑥 + 8 .

Q5:

Solve the following inequality: − 2 ≥ 𝑥 0 . 8 .

  • A 𝑥 ≥ − 2 . 5
  • B 𝑥 ≥ − 2 . 8
  • C 𝑥 ≥ − 1 . 6
  • D 𝑥 ≤ − 1 . 6
  • E 𝑥 ≤ − 2 . 8

Q6:

Write an inequality to describe the following, and then solve it: The quotient of a number and 9 is more than 2.

  • A 2 𝑥 < 1 9 , 𝑥 < 1 1 8
  • B 𝑥 9 < 2 , 𝑥 < 1 8
  • C 2 𝑥 > 1 9 , 𝑥 > 1 1 8
  • D 𝑥 9 > 2 , 𝑥 > 1 8
  • E 𝑥 9 ≤ 2 , 𝑥 ≤ 1 8

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