Lesson Worksheet: One-Variable Quadratic Inequalities Mathematics

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

Q1:

Solve 𝑥2𝑥<0 graphically.

  • A𝑅(0,2)
  • B{0,2}
  • C[0,2]
  • D(0,2)
  • E𝑅[0,2]

Q2:

Solve 𝑥𝑥6<0.

  • A[2,3]
  • B𝑅(2,3)
  • C𝑅[2,3]
  • D{2,3}
  • E(2,3)

Q3:

Solve 5(𝑥1)𝑥(7𝑥)𝑥 graphically.

  • A(2.5,)
  • B(0,2.5)
  • C[2.5,)
  • D(,2.5]
  • E[2.5,0)

Q4:

Solve 𝑥𝑥6>0 graphically.

  • A[2,3]
  • B{2,3}
  • C𝑅(2,3)
  • D(2,3)
  • E𝑅[2,3]

Q5:

Solve 𝑥+9>0 graphically.

  • A[3,3]
  • B𝑅[3,3]
  • C(3,3)
  • D{3,3}
  • E𝑅(3,3)

Q6:

Solve (23𝑥)(𝑥1)4(𝑥2) graphically.

  • A,454+5,
  • B,454+5,
  • C,454+5,
  • D,45
  • E4+5,

Q7:

Solve 2𝑥<3𝑥+5 graphically.

  • A1,52
  • B𝑅1,52
  • C1,52
  • D𝑅1,52
  • E1,52

Q8:

Solve (2𝑥)(𝑥1)2(𝑥1) graphically.

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

Q9:

Find all solutions to the inequality 𝑥+1210. Write your answer as an interval.

  • A[11,11]
  • B(11,11)
  • C(11,11)
  • D
  • E[11,11]

Q10:

Solve the inequality 𝑥𝑥12<0.

  • A𝑥[3,4]
  • B𝑥(4,3)
  • C𝑥(3,4)
  • D𝑥[3,4]
  • E𝑥[4,3]

Q11:

Write the interval describing all solutions to the inequality 30+13𝑥𝑥>0.

  • A(15,2)
  • B[15,2]
  • C(2,15)
  • D(15,2)
  • E[2,15]

Q12:

Solve the inequality 2𝑥+𝑥6.

  • A32,2
  • B32,2
  • C32,2
  • D32,2

Q13:

Find all solutions to the inequality (𝑥+4)+(𝑥+1)(𝑥16)<0. Write your answer as an interval.

  • A72,0
  • B0,72
  • C72,0
  • D72,0

Q14:

Which of the following describes the solution set of the inequality 𝑥7𝑥+12>0?

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

Q15:

Solve the inequality (𝑥+9)(𝑥2)22𝑥74.

  • A𝑥[7,8]
  • B𝑥(7,8)
  • C𝑥{7,8}
  • D𝑥[7,8]
  • E𝑥(7,8)

Q16:

Find the interval describing all solutions to the inequality 𝑥4.

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

Q17:

Find the interval containing all solutions to the inequality 64𝑥<0.

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

Q18:

Determine the solution set of the inequality (𝑥+3)<(5𝑥9).

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

Q19:

Write the interval describing all solutions to the inequality 𝑥2𝑥+1680.

  • A[12,14]
  • B(14,12)
  • C[14,12]
  • D(14,12)
  • E[14,12]

Q20:

Solve the inequality (𝑥5)(𝑥7)5𝑥+35.

  • A𝑥(0,7)
  • B𝑥[0,7]
  • C𝑥{0,7}
  • D𝑥(0,7)
  • E𝑥[0,7]

Q21:

Write the interval containing all solutions to the inequality 60+17𝑥𝑥0.

  • A(20,3)
  • B(3,20)
  • C(20,3)
  • D[20,3]
  • E[3,20]

Q22:

Solve 𝑥3𝑥40.

  • A[1,4]
  • B𝑅[1,4]
  • C𝑅(1,4)
  • D{1,4}
  • E(1,4)

Q23:

Solve 𝑥8𝑥+150 graphically.

  • A(3,5)
  • B(3,5)
  • C[3,5]
  • D{3,5}
  • E[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, 𝑤.

  • A𝑤(𝑤+9)20
  • B𝑤(𝑤+9)20
  • C𝑤(𝑤9)>20
  • D𝑤(2𝑤+9)20
  • E𝑤(𝑤9)20

Q25:

Find all solutions to the inequality (𝑥+4)<1369(𝑥+4). Write your answer as an interval.

  • A(21,4)
  • B[12,13]
  • C(21,4)
  • D[21,4]
  • E(12,13)

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