Solving Quadratic Inequalities Algebraically

2x² + 9x - 143 < 0

• -11 < x < 6.5

• -11 ≤ x ≤ 6.5

• no solution

• all reals

x² - 9x - 112 ≥ 0

• -7 < x < 16

• -7 ≤ x ≤ 16

• x < -7 or x > 16

• x ≤ -7 or x ≥ 16

-3x² + 45 ≥ 6x

• -5 < x < 3

• -5 ≤ x ≤ 3

• x < -5 or x > 3

• x ≤ -5 or x ≥ 3

4x² - 8x < 77

• -3.5 < x < 5.5

• -2.5 < x < 7.5

• -4 < x < 8

• -6 < x < 8

6x² - 54 ≤ 0

• -3 ≤ x ≤ 3

• x ≤ -3 or x ≥ 3

• -3 < x < 3

• x < -3 or x > 3

5x² + 10x + 7 ≥ 0

• no solution

• all reals

• x ≤ 5 or x ≥ 7

• 5 ≤ x ≤ 7

-3x² + 6x - 3 > 0

• no solution

• all reals

• x = 1

• x ≠ 1

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

• -5 < x < 7

• -3 ≤ x ≤ 12

• 4 < x < 15

• -2 < x < 10

-3x² + 3x - 6 ≤ 0

• no solution

• all reals

• x = 1

• x ≠ 1

-8x² - 9 ≥ 0

• no solution

• all reals

• x = 1.125

• x ≠ 1.125