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 + 3 𝑥 1 > 0 ?

  • A all real numbers
  • B 3 < 𝑥 < 1
  • C There are no values of 𝑥 for which the inequality holds.
  • D 𝑥 < 3 or 𝑥 > 1
  • E 𝑥 > 1

Q2:

Solve the inequality .

  • A
  • B
  • C
  • D
  • E

Q3:

Solve the inequality 𝑥 1 ( 𝑥 + 1 ) ( 𝑥 3 ) > 0 .

  • A ( , 1 ) ( 3 , )
  • B ( , 1 ) ( 3 , )
  • C ( , 1 ) ( 1 , 3 )
  • D ( 1 , 1 ) ( 3 , )
  • E ( , 1 ) ( 1 , )

Q4:

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

  • A 𝑥 3 or 𝑥 < 1
  • B 𝑥 3
  • C 0 < 𝑥 3
  • D 1 < 𝑥 3
  • Eall real numbers

Q5:

Find all the possible values of 𝑥 that satisfy 9 𝑥 > 9 4 given 𝑥 .

  • A 0 , 1 , 2 , 3 o r
  • B9
  • C3
  • D 1 , 2 , 3 o r

Q6:

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

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

Q7:

Given that 𝑥 is a whole number and 1 1 1 3 < 1 1 𝑥 < 1 , what are the possible values of 𝑥 ?

  • A 11
  • B 14
  • C 18
  • D 12

Q8:

Solve the inequality 𝑥 4 𝑥 + 3 𝑥 + 2 0 .

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

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