Solving Quadratic Inequalities

6x² - 54 ≤ 0

• -3 ≤ x ≤ 3
• x ≤ -3 or x ≥ 3
• -3 < x < 3
• x < -3 or x > 3

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

5x² + 10x + 7 ≥ 0

• no solution
• all reals
• x ≤ 5 or x ≥ 7
• 5 ≤ x ≤ 7

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

-3x² + 6x - 3 > 0

• no solution
• all reals
• x = 1
• x ≠ 1

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

8x + 140 > 4x^{2
hint: put squared term on the LEFT!}

• -5 < x < 7
• -3 ≤ x ≤ 12
• 4 < x < 15
• -2 < x < 10

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.B.4

2x² + 9x - 143 < 0

• -11 < x < 6.5
• -11 ≤ x ≤ 6.5
• no solution
• all reals

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

x² - 9x - 112 ≥ 0

• -7 < x < 16
• -7 ≤ x ≤ 16
• x < -7 or x > 16
• x ≤ -7 or x ≥ 16

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.4

-3x² + 45 ≥ 6x

• -5 < x < 3
• -5 ≤ x ≤ 3
• x < -5 or x > 3
• x ≤ -5 or x ≥ 3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

-3x² + 3x - 6 ≤ 0

• no solution
• all reals
• x = 1
• x ≠ 1

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

-8x² - 9 ≥ 0

• no solution
• all reals
• x = 1.125
• x ≠ 1.125

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

4x² - 8x < 77

• -3.5 < x < 5.5
• -2.5 < x < 7.5
• -4 < x < 8
• -6 < x < 8

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4