Worksheet: Inequalities on a Number Line

In this worksheet, we will practice finding and deducing the one-variable linear inequality from a specific given interval represented on the number line.

Q1:

What inequality is represented on the given figure?

  • A 𝑥 4
  • B 𝑥 > 4
  • C 𝑥 < 4
  • D 𝑥 4

Q2:

Which part of the shown line represents the set of solutions to the inequality 𝑥>5?

  • AA
  • BB

Q3:

Which of the following inequalities have been represented on the number line?

  • A 𝑥 1 or 𝑥>2
  • B 𝑥 < 1 or 𝑥>2
  • C 𝑥 1 and 𝑥>2
  • D 1 𝑥 < 2
  • E 1 < 𝑥 < 2

Q4:

Which part of the shown line represents the set of solutions to the inequality 𝑥<27?

  • AB
  • BA

Q5:

Which of the following diagrams represents the inequality 2𝑥<1?

  • A
  • B
  • C
  • D

Q6:

What inequality is represented on the given figure?

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

Q7:

Which inequality is represented on this number line?

  • A 𝑥 > 1
  • B 𝑥 < 1
  • C 𝑥 1
  • D 𝑥 1

Q8:

Which part of the shown line represents the set of solutions to the inequality 3<𝑥<56?

  • AA
  • BB
  • CC

Q9:

What inequality is represented on the given figure?

  • A 𝑥 < 2
  • B 𝑥 2
  • C 𝑥 > 2
  • D 𝑥 2

Q10:

What inequality is represented on the given figure?

  • A 𝑥 0
  • B 𝑥 > 0
  • C 𝑥 < 0
  • D 𝑥 0

Q11:

What inequality is represented on the given figure?

  • A 𝑥 < 4
  • B 𝑥 4
  • C 𝑥 > 4
  • D 𝑥 4

Q12:

What inequality is represented on the given figure?

  • A 𝑥 4
  • B 𝑥 > 4
  • C 𝑥 < 4
  • D 𝑥 4

Q13:

What inequality is represented on the given figure?

  • A 𝑥 < 4
  • B 𝑥 4
  • C 𝑥 > 4
  • D 𝑥 4

Q14:

What inequality is represented on the given figure?

  • A 𝑥 4
  • B 𝑥 4
  • C 𝑥 < 4
  • D 𝑥 > 4

Q15:

What inequality is represented on the given figure?

  • A 𝑥 4
  • B 𝑥 < 4
  • C 𝑥 > 4
  • D 𝑥 4

Q16:

What inequality is represented on the given figure?

  • A 𝑥 3
  • B 𝑥 3
  • C 𝑥 < 3
  • D 𝑥 > 3

Q17:

What inequality is represented on the given figure?

  • A 𝑥 1
  • B 𝑥 1
  • C 𝑥 < 1
  • D 𝑥 > 1

Q18:

The situation where 𝑥 has to be at least 2 away from 1 can be expressed by the compound inequality 𝑥1<2 or 𝑥1>2. Which of the following number lines represents this inequality?

  • A
  • B
  • C
  • D

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