Worksheet: One-Variable Quadratic Inequalities

In this worksheet, we will practice solving one-variable quadratic inequalities algebraically and graphically.

Q1:

Solve π‘₯βˆ’2π‘₯<0 graphically.

  • A(0,2)
  • Bπ‘…βˆ’(0,2)
  • Cπ‘…βˆ’[0,2]
  • D[0,2]
  • E{0,2}

Q2:

Solve π‘₯βˆ’π‘₯βˆ’6<0.

  • A[βˆ’2,3]
  • Bπ‘…βˆ’(βˆ’2,3)
  • Cπ‘…βˆ’[βˆ’2,3]
  • D{βˆ’2,3}
  • E(βˆ’2,3)

Q3:

Solve 5(π‘₯βˆ’1)βˆ’π‘₯(7βˆ’π‘₯)≀π‘₯ graphically.

  • A(βˆ’2.5,∞)
  • B(0,2.5)
  • C[βˆ’2.5,∞)
  • D(βˆ’βˆž,2.5]
  • E[βˆ’2.5,0)

Q4:

Solve π‘₯βˆ’π‘₯βˆ’6>0 graphically.

  • A[βˆ’2,3]
  • B{βˆ’2,3}
  • Cπ‘…βˆ’(βˆ’2,3)
  • D(βˆ’2,3)
  • Eπ‘…βˆ’[βˆ’2,3]

Q5:

Solve βˆ’π‘₯+9>0 graphically.

  • A[βˆ’3,3]
  • Bπ‘…βˆ’[βˆ’3,3]
  • C(βˆ’3,3)
  • D{βˆ’3,3}
  • Eπ‘…βˆ’(βˆ’3,3)

Q6:

Solve (2βˆ’3π‘₯)βˆ’(π‘₯βˆ’1)β‰₯βˆ’4βˆ’(π‘₯βˆ’2) graphically.

  • Aο€»βˆ’βˆž,4βˆ’βˆš5βˆͺο€»4+√5,βˆžο‡
  • Bο€»βˆ’βˆž,4βˆ’βˆš5βˆͺ4+√5,βˆžο‡
  • Cο€»βˆ’βˆž,4βˆ’βˆš5βˆͺο€»4+√5,βˆžο‡
  • Dο€»βˆ’βˆž,4βˆ’βˆš5
  • Eο€»4+√5,βˆžο‡

Q7:

Solve 2π‘₯<3π‘₯+5 graphically.

  • Aο€Όβˆ’1,52
  • Bπ‘…βˆ’ο”βˆ’1,52
  • Cο”βˆ’1,52
  • Dπ‘…βˆ’ο€Όβˆ’1,52
  • Eο¬βˆ’1,52

Q8:

Solve (2βˆ’π‘₯)(π‘₯βˆ’1)β‰₯2βˆ’(π‘₯βˆ’1) graphically.

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

Q9:

Find all solutions to the inequality π‘₯+121≀0. Write your answer as an interval.

  • A[βˆ’11,11]
  • B(βˆ’11,11)
  • Cβ„βˆ’(βˆ’11,11)
  • Dβˆ…
  • Eβ„βˆ’[βˆ’11,11]

Q10:

Solve the inequality π‘₯βˆ’π‘₯βˆ’12<0.

  • Aπ‘₯∈[βˆ’3,4]
  • Bπ‘₯∈(βˆ’4,3)
  • Cπ‘₯∈(βˆ’3,4)
  • Dπ‘₯βˆˆβ„βˆ’[βˆ’3,4]
  • Eπ‘₯∈[βˆ’4,3]

Q11:

Write the interval describing all solutions to the inequality 30+13π‘₯βˆ’π‘₯>0.

  • Aβ„βˆ’(βˆ’15,2)
  • Bβ„βˆ’[βˆ’15,2]
  • C(βˆ’2,15)
  • D(βˆ’15,2)
  • E[βˆ’2,15]

Q12:

Solve the inequality βˆ’2π‘₯+π‘₯β‰₯βˆ’6.

  • Aβ„βˆ’ο€Όβˆ’32,2
  • Bβ„βˆ’ο”βˆ’32,2
  • Cο€Όβˆ’32,2
  • Dο”βˆ’32,2

Q13:

Find all solutions to the inequality (π‘₯+4)+(π‘₯+1)(π‘₯βˆ’16)<0. Write your answer as an interval.

  • Aο”βˆ’72,0
  • Bο€Ό0,72
  • Cβ„βˆ’ο€Όβˆ’72,0
  • Dβ„βˆ’ο”βˆ’72,0

Q14:

Which of the following describes the solution set of the inequality π‘₯βˆ’7π‘₯+12>0?

  • Aβ„βˆ’(3,4)
  • Bβ„βˆ’[βˆ’4,βˆ’3]
  • Cβ„βˆ’(βˆ’4,βˆ’3)
  • D[3,4]
  • Eβ„βˆ’[3,4]

Q15:

Solve the inequality (π‘₯+9)(π‘₯βˆ’2)≀22π‘₯βˆ’74.

  • Aπ‘₯βˆˆβ„βˆ’[7,8]
  • Bπ‘₯βˆˆβ„βˆ’(7,8)
  • Cπ‘₯∈{7,8}
  • Dπ‘₯∈[7,8]
  • Eπ‘₯∈(7,8)

Q16:

Find the interval describing all solutions to the inequality π‘₯≀4.

  • A(βˆ’2,2)
  • B[βˆ’2,2]
  • Cβ„βˆ’[βˆ’2,2]
  • Dβ„βˆ’(βˆ’2,2)

Q17:

Find the interval describing all solutions to the inequality 64βˆ’π‘₯<0.

  • Aβ„βˆ’(βˆ’8,8)
  • B(βˆ’8,8)
  • C[βˆ’8,8]
  • Dβ„βˆ’[βˆ’8,8]

Q18:

Determine the solution set of the inequality (π‘₯+3)<(5π‘₯βˆ’9).

  • A(1,3)
  • B[1,3]
  • Cβ„βˆ’(1,3)
  • Dβ„βˆ’[1,3]

Q19:

Write the interval describing all solutions to the inequality βˆ’π‘₯βˆ’2π‘₯+168β‰₯0.

  • A[βˆ’12,14]
  • Bβ„βˆ’(βˆ’14,12)
  • Cβ„βˆ’[βˆ’14,12]
  • D(βˆ’14,12)
  • E[βˆ’14,12]

Q20:

Solve the inequality (π‘₯βˆ’5)(π‘₯βˆ’7)β‰₯βˆ’5π‘₯+35.

  • Aπ‘₯∈(0,7)
  • Bπ‘₯∈[0,7]
  • Cπ‘₯βˆˆβ„βˆ’{0,7}
  • Dπ‘₯βˆˆβ„βˆ’(0,7)
  • Eπ‘₯βˆˆβ„βˆ’[0,7]

Q21:

Write the interval describing all solutions to the inequality 60+17π‘₯βˆ’π‘₯≀0.

  • A(βˆ’20,3)
  • Bβ„βˆ’(βˆ’3,20)
  • Cβ„βˆ’(βˆ’20,3)
  • Dβ„βˆ’[βˆ’20,3]
  • E[βˆ’3,20]

Q22:

Solve π‘₯βˆ’3π‘₯βˆ’4≀0.

  • A[βˆ’1,4]
  • Bπ‘…βˆ’[βˆ’1,4]
  • Cπ‘…βˆ’(βˆ’1,4)
  • D{βˆ’1,4}
  • E(βˆ’1,4)

Q23:

Solve π‘₯βˆ’8π‘₯+15β‰₯0 graphically.

  • Aβ„βˆ’(3,5)
  • B(3,5)
  • C[3,5]
  • D{3,5}
  • Eβ„βˆ’[3,5]

Q24:

The length of a rectangle is nine more than its width; the area of the rectangle is no more than 20. Write an inequality for the area of the rectangle, 𝐴, in terms of the width, 𝑀.

  • A𝑀(𝑀+9)β‰₯20
  • B𝑀(𝑀+9)≀20
  • C𝑀(π‘€βˆ’9)>20
  • D𝑀(2𝑀+9)β‰₯20
  • E𝑀(π‘€βˆ’9)β‰₯20

Q25:

Find all solutions to the inequality (π‘₯+4)<136βˆ’9(π‘₯+4). Write your answer as an interval.

  • Aβ„βˆ’(βˆ’21,4)
  • Bβ„βˆ’[βˆ’12,13]
  • C(βˆ’21,4)
  • D[βˆ’21,4]
  • Eβ„βˆ’(βˆ’12,13)

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