Lesson Worksheet: Rational Inequalities Mathematics • 10th Grade

In this worksheet, we will practice solving rational inequalities.


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

  • Aπ‘₯>βˆ’1
  • BThere are no values of π‘₯ for which the inequality holds.
  • Call real numbers
  • Dβˆ’3<π‘₯<1
  • Eπ‘₯<βˆ’3 or π‘₯>1


Solve the inequality π‘₯βˆ’1(π‘₯+1)(π‘₯βˆ’3)≀13.

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


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

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


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

  • Aall real numbers
  • B0<π‘₯≀3
  • Cπ‘₯β‰₯3 or π‘₯<1
  • D1<π‘₯≀3
  • Eπ‘₯≀3


Find all the possible values of π‘₯ that satisfy 9π‘₯>94 given π‘₯βˆˆβ„•.

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


Solve the inequality 0<π‘₯βˆ’1(π‘₯+1)(π‘₯βˆ’3)≀13.

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


Given that π‘₯ is a whole number and 1113<11π‘₯<1, what are the possible values of π‘₯?

  • A14
  • B18
  • C12
  • D11


Find algebraically the solution set of the inequality 1|4π‘₯βˆ’9|>17.

  • Aο€Ό0,7734οˆβˆ’ο¬94
  • Bο€Ό3817,7734οˆβˆ’ο¬94
  • Cο€Όβˆ’7734,7734οˆβˆ’ο¬49
  • Dο€Όβˆ’3817,7734οˆβˆ’ο¬94


Solve the inequality 12π‘₯+3π‘₯<0.

  • Aο€Όβˆ’32,0
  • Bβ„βˆ’ο”βˆ’32,0
  • C(0,∞)
  • Dβ„βˆ’ο”βˆ’23,0
  • Eο€Όβˆ’23,0


Solve the inequality π‘₯2π‘₯βˆ’3<0.

  • Aβ„βˆ’ο”0,32
  • Bβ„βˆ’ο”0,23
  • Cο€Ό0,23
  • Dο€Ό0,32
  • E(0,∞)

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