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?

  • A 𝑥 > − 1
  • BThere are no values of 𝑥 for which the inequality holds.
  • Call real numbers
  • D − 3 < 𝑥 < 1
  • E 𝑥 < − 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
  • B 0 < 𝑥 ≤ 3
  • C 𝑥 ≥ 3 or 𝑥<1
  • D 1 < 𝑥 ≤ 3
  • E 𝑥 ≤ 3

Q5:

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

  • A 1 , 2 , 3 o r
  • B 0 , 1 , 2 , 3 o r
  • 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.

  • A 0 , 7 7 3 4 − 9 4
  • B 3 8 1 7 , 7 7 3 4 − 9 4
  • C − 7 7 3 4 , 7 7 3 4 − 4 9
  • D − 3 8 1 7 , 7 7 3 4 − 9 4

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