Worksheet: Rational Inequalities

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In this worksheet, we will practice solving rational inequalities.

Q1:

What are all the values of 𝑥 for which it is true that 𝑥+3𝑥−1>0?

  • A𝑥>−1
  • BThere are no values of 𝑥 for which the inequality holds.
  • Call real numbers
  • D−3<𝑥<1
  • E𝑥<−3 or 𝑥>1

Q2:

Solve the inequality 𝑥−1(𝑥+1)(𝑥−3)≤13.

  • A(−∞,−1)∪(0,3)∪(5,∞)
  • B(−∞,−1)∪[5,∞)
  • C(−∞,−1)∪[0,3)∪[5,∞)
  • D(0,3)∪(5,∞)
  • E[0,3)∪[5,∞)

Q3:

Solve the inequality 𝑥−1(𝑥+1)(𝑥−3)>0.

  • A(−∞,−1)∪(1,3)
  • B(−∞,1)∪(3,∞)
  • C(−∞,−1)∪(1,∞)
  • D(−1,1)∪(3,∞)
  • E(−∞,−1)∪(3,∞)

Q4:

What are all the values of 𝑥 for which it is true that 𝑥+3𝑥−1≥3?

  • Aall real numbers
  • B0<𝑥≤3
  • C𝑥≥3 or 𝑥<1
  • D1<𝑥≤3
  • E𝑥≤3

Q5:

Find all the possible values of 𝑥 that satisfy 9𝑥>94 given 𝑥∈ℕ.

  • A1,2,3or
  • B0,1,2,3or
  • C9
  • D3

Q6:

Solve the inequality 0<𝑥−1(𝑥+1)(𝑥−3)≤13.

  • A[0,∞)
  • B[0,1)∪[3,∞)
  • C[0,1)∪[5,∞)
  • D(0,1)∪(3,∞)
  • E(0,1)∪(5,∞)

Q7:

Given that 𝑥 is a whole number and 1113<11𝑥<1, what are the possible values of 𝑥?

  • A14
  • B18
  • C12
  • D11

Q8:

Solve the inequality 𝑥−4𝑥+3𝑥+2≤0.

  • A(−∞,−2]∪[3,∞)
  • B[−2,3]
  • C(−∞,−2)∪[1,3]
  • D[1,3]

Q9:

Find algebraically the solution set of the inequality 1|4𝑥−9|>17.

  • A0,7734−94
  • B3817,7734−94
  • C−7734,7734−49
  • D−3817,7734−94

Q10:

Solve the inequality 12𝑥+3𝑥<0.

  • A−32,0
  • Bℝ−−32,0
  • C(0,∞)
  • Dℝ−−23,0
  • E−23,0

Q11:

Solve the inequality 𝑥2𝑥−3<0.

  • Aℝ−0,32
  • Bℝ−0,23
  • C0,23
  • D0,32
  • E(0,∞)

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