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?

  • 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 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
  • 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.

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

  • 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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