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Lesson: Rational Inequalities

Sample Question Videos

Worksheet • 8 Questions • 4 Videos

Q1:

What are all the values of π‘₯ for which it is true that π‘₯ + 3 π‘₯ βˆ’ 1 > 0 ?

  • A π‘₯ < βˆ’ 3 or π‘₯ > 1
  • B π‘₯ > βˆ’ 1
  • C βˆ’ 3 < π‘₯ < 1
  • D There are no values of π‘₯ for which the inequality holds.
  • E all real numbers

Q2:

Solve the inequality .

  • A
  • B
  • C
  • D
  • E

Q3:

Solve the inequality π‘₯ βˆ’ 1 ( π‘₯ + 1 ) ( π‘₯ βˆ’ 3 ) > 0 .

  • A ( βˆ’ 1 , 1 ) βˆͺ ( 3 , ∞ )
  • B ( βˆ’ ∞ , βˆ’ 1 ) βˆͺ ( 1 , ∞ )
  • C ( βˆ’ ∞ , 1 ) βˆͺ ( 3 , ∞ )
  • D ( βˆ’ ∞ , βˆ’ 1 ) βˆͺ ( 1 , 3 )
  • E ( βˆ’ ∞ , βˆ’ 1 ) βˆͺ ( 3 , ∞ )

Q4:

What are all the values of π‘₯ for which it is true that π‘₯ + 3 π‘₯ βˆ’ 1 β‰₯ 3 ?

  • A 1 < π‘₯ ≀ 3
  • Ball real numbers
  • C π‘₯ ≀ 3
  • D 0 < π‘₯ ≀ 3
  • E π‘₯ β‰₯ 3 or π‘₯ < 1

Q5:

Find all the possible values of π‘₯ that satisfy 9 π‘₯ > 9 4 given π‘₯ ∈ β„• .

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

Q6:

Solve the inequality 0 < π‘₯ βˆ’ 1 ( π‘₯ + 1 ) ( π‘₯ βˆ’ 3 ) ≀ 1 3 .

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

Q7:

Given that π‘₯ is a whole number and 1 1 1 3 < 1 1 π‘₯ < 1 , what are the possible values of π‘₯ ?

  • A 12
  • B 14
  • C 18
  • D 11

Q8:

Solve the inequality π‘₯ βˆ’ 4 π‘₯ + 3 π‘₯ + 2 ≀ 0 2 .

  • A ( βˆ’ ∞ , βˆ’ 2 ) βˆͺ [ 1 , 3 ]
  • B [ 1 , 3 ]
  • C ( βˆ’ ∞ , βˆ’ 2 ] βˆͺ [ 3 , + ∞ )
  • D [ βˆ’ 2 , 3 ]
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