Worksheet: Solving Linear Inequalities

In this worksheet, we will practice solving linear inequalities by applying inverse operations.

Q1:

If 𝑥 8 > 3 , then 𝑥 > .

Q2:

Which one of the following numbers satisfies the inequality 𝑥 > 6 ?

  • A 1 0
  • B 1 1
  • C 9
  • D 5

Q3:

Which of the following does not satisfy the inequality 𝑥 1 ?

  • A 3
  • B 4
  • C 1
  • D2

Q4:

Which of the following inequalities is equivalent to 5 𝑥 < 4 ?

  • A 𝑥 = 4 5
  • B 𝑥 < 2 0
  • C 𝑥 > 4 5
  • D 𝑥 < 4 5
  • E 𝑥 4 5

Q5:

Which of the following inequalities is equivalent to 4 𝑥 5 ?

  • A 𝑥 5 4
  • B 𝑥 2 0
  • C 𝑥 < 5 4
  • D 𝑥 5 4

Q6:

Solve the following inequality: 1 0 𝑥 6 0 .

  • A 𝑥 6
  • B 𝑥 6
  • C 𝑥 6
  • D 𝑥 6

Q7:

Which of the following inequalities has a solution of 𝑝 > 3 0 ?

  • A 𝑝 + 4 7 > 1 7
  • B 𝑝 1 7 > 4 7
  • C 𝑝 + 4 7 > 1 7
  • D 𝑝 + 1 7 > 4 7
  • E 𝑝 8 > 3 8

Q8:

Which of the following inequalities has a solution that involves reversing its sign?

  • A 1 1 𝑥 > 1 9
  • B 1 4 𝑥 > 1 6
  • C 1 3 𝑥 > 2 5
  • D 1 2 𝑥 > 3 4
  • E 9 𝑥 > 3 5

Q9:

Which one of the following numbers satisfies the inequality 𝑥 > 1 ?

  • A 3
  • B 5
  • C 4
  • D 0

Q10:

Which one of the following numbers satisfies the inequality 𝑥 > 2 ?

  • A 4
  • B 5
  • C 7
  • D 1

Q11:

Which of the following inequalities has a solution that involves reversing its sign?

  • A 9 𝑥 < 1 9
  • B 1 1 𝑥 < 3 3
  • C 1 4 𝑥 < 2 3
  • D 8 𝑥 < 1 6
  • E 5 𝑥 < 2 1

Q12:

Which of the following does not satisfy the inequality 𝑥 8 ?

  • A 1 0
  • B 1 1
  • C 8
  • D 6

Q13:

Which of the following inequalities is equivalent to 3 𝑥 < 2 ?

  • A 𝑥 = 2 3
  • B 𝑥 < 6
  • C 𝑥 > 2 3
  • D 𝑥 < 2 3
  • E 𝑥 2 3

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