Worksheet: Quadratic Inequalities

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

Q1:

Solve the inequality 2 𝑥 + 𝑥 6 .

  • 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 .

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

Q3:

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

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

Q4:

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

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

Q5:

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

  • 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 .

  • 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 ) .

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

Q9:

Given 𝑓 = 3 𝑥 9 𝑥 + 6 , 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 cell phone company has the following cost and revenue functions: 𝐶 ( 𝑥 ) = 8 𝑥 6 0 0 𝑥 + 2 1 5 0 0 and 𝑅 ( 𝑥 ) = 3 𝑥 + 4 8 0 𝑥 , where 𝑥 is the number of cell phones. State the range for the number of cell phones they can produce while making a profit. Round your answers to the nearest integer that guarantees a profit.

  • A28–71 cell phones
  • B28–70 cell phones
  • Cmore than 160 cell phones
  • D27–70 cell 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 }

Q12:

Find all solutions to the inequality ( 𝑥 + 4 ) + ( 𝑥 + 1 ) ( 𝑥 1 6 ) < 0 . Write your answer as an interval.

  • A 0 , 7 2
  • B 7 2 , 0
  • C 7 2 , 0
  • D 7 2 , 0

Q13:

Write the interval describing all solutions to the inequality 6 0 + 1 7 𝑥 𝑥 0 .

  • A ( 2 0 , 3 )
  • B ( 3 , 2 0 )
  • C [ 2 0 , 3 ]
  • D ( 2 0 , 3 )
  • E [ 3 , 2 0 ]

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