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?

  • A𝑥4
  • B𝑥>4
  • C𝑥<4
  • D𝑥4

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?

  • A𝑥1 or 𝑥>2
  • B𝑥<1 or 𝑥>2
  • C𝑥1 and 𝑥>2
  • D1𝑥<2
  • E1<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?

  • A4<𝑥2
  • B4𝑥<2
  • C4<𝑥<2
  • D4𝑥2

Q7:

Which inequality is represented on this number line?

  • A𝑥>1
  • B𝑥<1
  • C𝑥1
  • D𝑥1

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?

  • A𝑥<2
  • B𝑥2
  • C𝑥>2
  • D𝑥2

Q10:

What inequality is represented on the given figure?

  • A𝑥0
  • B𝑥>0
  • C𝑥<0
  • D𝑥0

Q11:

What inequality is represented on the given figure?

  • A𝑥<4
  • B𝑥4
  • C𝑥>4
  • D𝑥4

Q12:

What inequality is represented on the given figure?

  • A𝑥4
  • B𝑥>4
  • C𝑥<4
  • D𝑥4

Q13:

What inequality is represented on the given figure?

  • A𝑥<4
  • B𝑥4
  • C𝑥>4
  • D𝑥4

Q14:

What inequality is represented on the given figure?

  • A𝑥4
  • B𝑥4
  • C𝑥<4
  • D𝑥>4

Q15:

What inequality is represented on the given figure?

  • A𝑥4
  • B𝑥<4
  • C𝑥>4
  • D𝑥4

Q16:

What inequality is represented on the given figure?

  • A𝑥3
  • B𝑥3
  • C𝑥<3
  • D𝑥>3

Q17:

What inequality is represented on the given figure?

  • A𝑥1
  • B𝑥1
  • C𝑥<1
  • D𝑥>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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