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Lesson Worksheet: Linear Inequalities Mathematics

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+72.

  • A𝑥3
  • B𝑥9
  • C𝑥3
  • D𝑥3
  • E𝑥3

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.

  • A𝑥34
  • B𝑥34
  • C𝑥43
  • D𝑥34
  • E𝑥34

Q5:

Find the set of values of 𝑥 that satisfy the inequality 2(3𝑥2)(2𝑥+4).

  • A𝑥0
  • B𝑥1
  • C𝑥1
  • D𝑥1
  • E𝑥0

Q6:

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

  • A𝑥3
  • B𝑥13
  • C𝑥13
  • D𝑥13
  • E𝑥13

Q7:

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

  • A{𝑥𝑥<9}
  • B{𝑥𝑥>1}
  • C{𝑥𝑥>9}
  • D𝑥𝑥>19
  • E{𝑥𝑥<1}

Q8:

Find the set of values of 𝑥 that satisfy the inequalities 2(𝑥3)<3𝑥+1 and 3(2𝑥1)11. Give your answer in set notation.

  • A𝑥𝑥73
  • B𝑥7𝑥<73
  • C{𝑥𝑥>7}
  • D𝑥7<𝑥73
  • E𝑥7>𝑥73

Q9:

Find the set of values of 𝑥 that satisfies either the inequality 2(𝑥1)3(𝑥5) or the inequality 5(𝑥+4)3(32𝑥). Give your answer in set notation.

  • A{𝑥𝑥1}{𝑥𝑥13}
  • B{𝑥𝑥1}{𝑥𝑥13}
  • C{𝑥𝑥1}{𝑥𝑥13}
  • D{𝑥𝑥1}{𝑥𝑥13}
  • E{𝑥𝑥1}{𝑥𝑥13}

Q10:

Find the set of values of 𝑥 that satisfies the inequalities 3(𝑥1)2(𝑥1) and 5(𝑥+3)>2(53𝑥). Give your answer in set notation.

  • A𝑥511<𝑥1
  • B𝑥511<𝑥1
  • C𝑥𝑥>511
  • D{𝑥𝑥1}
  • E𝑥1<𝑥511

This lesson includes 90 additional question variations for subscribers.

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