Worksheet: Inequalities on a Number Line

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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?

  • A𝑥≤4
  • B𝑥>4
  • C𝑥<4
  • D𝑥≥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?

  • A𝑥≤−1 or 𝑥>2
  • B𝑥<−1 or 𝑥>2
  • C𝑥≤−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 −2≤𝑥<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?

  • A𝑥>−1
  • B𝑥<−1
  • C𝑥≥−1
  • D𝑥≤−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?

  • A𝑥<−2
  • B𝑥≤−2
  • C𝑥>−2
  • D𝑥≥−2

Q10:

What inequality is represented on the given figure?

  • A𝑥≤0
  • B𝑥>0
  • C𝑥<0
  • D𝑥≥0

Q11:

What inequality is represented on the given figure?

  • A𝑥<−4
  • B𝑥≤−4
  • C𝑥>−4
  • D𝑥≥−4

Q12:

What inequality is represented on the given figure?

  • A𝑥≤−4
  • B𝑥>−4
  • C𝑥<−4
  • D𝑥≥−4

Q13:

What inequality is represented on the given figure?

  • A𝑥<4
  • B𝑥≤4
  • C𝑥>4
  • D𝑥≥4

Q14:

What inequality is represented on the given figure?

  • A𝑥≤−4
  • B𝑥≥−4
  • C𝑥<−4
  • D𝑥>−4

Q15:

What inequality is represented on the given figure?

  • A𝑥≤4
  • B𝑥<4
  • C𝑥>4
  • D𝑥≥4

Q16:

What inequality is represented on the given figure?

  • A𝑥≤3
  • B𝑥≥3
  • C𝑥<3
  • D𝑥>3

Q17:

What inequality is represented on the given figure?

  • A𝑥≤−1
  • B𝑥≥−1
  • 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 𝑥−1<−2 or 𝑥−1>2. Which of the following number lines represents this inequality?

  • A
  • B
  • C
  • D

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