Lesson Worksheet: Linear Inequalities Mathematics

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In this worksheet, we will practice solving linear inequalities and two linear inequalities combined using “and” or “or” in one variable.

Q1:

Find the set of values of 𝑥 that satisfy the inequality 3𝑥+7≤−2.

  • A𝑥≥−3
  • B𝑥≤−9
  • C𝑥≤−3
  • D𝑥≥3
  • E𝑥≤3

Q2:

Find the set of values of 𝑥 that satisfies the inequality −2𝑥+5>2.

  • A𝑥>−32
  • B𝑥<32
  • C𝑥>32
  • D𝑥<3
  • E𝑥>−3

Q3:

Find the set of values of 𝑥 that satisfies the inequality −4𝑥+5>−2𝑥+1.

  • A𝑥>−2
  • B𝑥<2
  • C𝑥>2
  • D𝑥<−4
  • E𝑥<−2

Q4:

Find the set of values of 𝑥 that satisfies the inequality 5(𝑥+1)≥𝑥+2.

  • A𝑥≥−34
  • B𝑥≥34
  • C𝑥≥−43
  • D𝑥≤−34
  • E𝑥≤34

Q5:

Find the set of values of 𝑥 that satisfy the inequality 2(3𝑥−2)≤−(2𝑥+4).

  • A𝑥≥0
  • B𝑥≤−1
  • C𝑥≤1
  • D𝑥≥1
  • E𝑥≤0

Q6:

Find the set of values of 𝑥 that satisfy the inequality −𝑥(𝑥+3)≤𝑥(6−𝑥)+3.

  • A𝑥≥−3
  • B𝑥≤−13
  • C𝑥≥13
  • D𝑥≥−13
  • E𝑥≤13

Q7:

Find the set of values of 𝑥 that satisfy the inequality 7𝑥+1>−2𝑥+10. Give your answer in set notation.

  • A{𝑥∶𝑥<9}
  • B{𝑥∶𝑥>1}
  • C{𝑥∶𝑥>9}
  • D𝑥∶𝑥>19
  • E{𝑥∶𝑥<1}

Q8:

Find the set of values of 𝑥 that satisfy the inequalities 2(𝑥−3)<3𝑥+1 and 3(2𝑥−1)≤11. Give your answer in set notation.

  • A𝑥∶𝑥≤73
  • B𝑥∶−7≤𝑥<73
  • C{𝑥∶𝑥>−7}
  • D𝑥∶−7<𝑥≤73
  • E𝑥∶−7>𝑥≥73

Q9:

Find the set of values of 𝑥 that satisfies either the inequality 2(𝑥−1)≤3(𝑥−5) or the inequality 5(𝑥+4)≤3(3−2𝑥). Give your answer in set notation.

  • A{𝑥∶𝑥≤−1}∩{𝑥∶𝑥≥13}
  • B{𝑥∶𝑥≥−1}∪{𝑥∶𝑥≥13}
  • C{𝑥∶𝑥≤−1}∪{𝑥∶𝑥≥13}
  • D{𝑥∶𝑥≤−1}∪{𝑥∶𝑥≤13}
  • E{𝑥∶𝑥≥−1}∩{𝑥∶𝑥≤13}

Q10:

Find the set of values of 𝑥 that satisfies the inequalities 3(𝑥−1)≤2(𝑥−1) and 5(𝑥+3)>2(5−3𝑥). Give your answer in set notation.

  • A𝑥∶−511<𝑥≤1
  • B𝑥∶511<𝑥≤1
  • C𝑥∶𝑥>−511
  • D{𝑥∶𝑥≤1}
  • E𝑥∶−1<𝑥≤511

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