Worksheet: Rational Inequalities

In this worksheet, we will practice solving rational inequalities.

Q1:

What are all the values of 𝑥 for which it is true that 𝑥+3𝑥1>0?

  • A𝑥>1
  • BThere are no values of 𝑥 for which the inequality holds.
  • Call real numbers
  • D3<𝑥<1
  • E𝑥<3 or 𝑥>1

Q2:

Solve the inequality 𝑥1(𝑥+1)(𝑥3)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 𝑥1(𝑥+1)(𝑥3)>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+3𝑥13?

  • Aall real numbers
  • B0<𝑥3
  • C𝑥3 or 𝑥<1
  • D1<𝑥3
  • E𝑥3

Q5:

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

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

Q6:

Solve the inequality 0<𝑥1(𝑥+1)(𝑥3)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 𝑥4𝑥+3𝑥+20.

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

Q9:

Find algebraically the solution set of the inequality 1|4𝑥9|>17.

  • A0,773494
  • B3817,773494
  • C7734,773449
  • D3817,773494

Q10:

Solve the inequality 12𝑥+3𝑥<0.

  • A32,0
  • B32,0
  • C(0,)
  • D23,0
  • E23,0

Q11:

Solve the inequality 𝑥2𝑥3<0.

  • A0,32
  • B0,23
  • C0,23
  • D0,32
  • E(0,)

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