Worksheet: Quadratic Inequalities

In this worksheet, we will practice solving quadratic inequalities in one variable algebraically.

Q1:

Solve the inequality 2 𝑥 + 𝑥 6 2 .

  • A 3 2 , 2
  • B 3 2 , 2
  • C 3 2 , 2
  • D 3 2 , 2

Q2:

Write the interval describing all solutions to the inequality 𝑥 2 𝑥 + 1 6 8 0 2 .

  • A ] 1 4 , 1 2 [
  • B [ 1 4 , 1 2 ]
  • C ] 1 4 , 1 2 [
  • D [ 1 4 , 1 2 ]
  • E [ 1 2 , 1 4 ]

Q3:

Which of the following describes the solution set of the inequality 𝑥 7 𝑥 + 1 2 > 0 2 ?

  • A [ 4 , 3 ]
  • B ] 3 , 4 [
  • C ] 4 , 3 [
  • D [ 3 , 4 ]
  • E [ 3 , 4 ]

Q4:

Write the interval describing all solutions to the inequality 3 0 + 1 3 𝑥 𝑥 > 0 2 .

  • A ] 1 5 , 2 [
  • B [ 1 5 , 2 ]
  • C ] 1 5 , 2 [
  • D ] 2 , 1 5 [
  • E [ 2 , 1 5 ]

Q5:

Find the interval describing all solutions to the inequality 𝑥 4 2 .

  • A ] 2 , 2 [
  • B [ 2 , 2 ]
  • C ] 2 , 2 [
  • D [ 2 , 2 ]

Q6:

Solve the inequality ( 𝑥 + 9 ) ( 𝑥 2 ) 2 2 𝑥 7 4 .

  • A 𝑥 ] 7 , 8 [
  • B 𝑥 { 7 , 8 }
  • C 𝑥 [ 7 , 8 ]
  • D 𝑥 [ 7 , 8 ]
  • E 𝑥 ] 7 , 8 [

Q7:

Find the interval describing all solutions to the inequality 6 4 𝑥 < 0 2 .

  • A ] 8 , 8 [
  • B [ 8 , 8 ]
  • C ] 8 , 8 [
  • D [ 8 , 8 ]

Q8:

Determine the solution set of the inequality ( 𝑥 + 3 ) < ( 5 𝑥 9 ) 2 2 .

  • A ] 1 , 3 [
  • B [ 1 , 3 ]
  • C ] 1 , 3 [
  • D [ 1 , 3 ]

Q9:

Given 𝑓 = 3 𝑥 9 𝑥 + 6 2 , find the solution set of the inequality 𝑓 ( 𝑥 ) < 0 by determining the sign of 𝑓 .

  • A 𝑓 ( 𝑥 ) is negative when 𝑥 [ 1 , 2 ] , which is the solution set of the inequality.
  • B 𝑓 ( 𝑥 ) is negative when 𝑥 [ 1 , 2 ] , which is the solution set of the inequality.
  • C 𝑓 ( 𝑥 ) is negative when 𝑥 ] 1 , 2 [ , which is the solution set of the inequality.
  • D 𝑓 ( 𝑥 ) is negative when 𝑥 ] 1 , 2 [ , which is the solution set of the inequality.

Q10:

A mobile phone company has the following cost and revenue functions: 𝐶 ( 𝑥 ) = 8 𝑥 6 0 0 𝑥 + 2 1 5 0 0 2 and 𝑅 ( 𝑥 ) = 3 𝑥 + 4 8 0 𝑥 2 . State the range for the number of mobile phones they can produce while making a profit. Round your answers to the nearest integer that guarantees a profit.

  • A28–71 mobile phones
  • B27–70 mobile phones
  • Cmore than 160 mobile phones
  • D28–70 mobile phones

Q11:

Solve the inequality ( 𝑥 5 ) ( 𝑥 7 ) 5 𝑥 + 3 5 .

  • A 𝑥 ] 0 , 7 [
  • B 𝑥 { 0 , 7 }
  • C 𝑥 [ 0 , 7 ]
  • D 𝑥 ] 0 , 7 [
  • E 𝑥 [ 0 , 7 ]

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