1. Solving Quadratic Inequalities algebraically

2. Solve a quadratic inequality
Solve x2 + x ≥ 12
1. Replace the inequality sign with equal sign
x2 + x = 12
2. Write the equation in standard form
x2 + x – 12 = 0
3. Factorize the quadratic
(x + 4)(x – 3) = 0
4. Solve using the zero product property
x = -4 or x = 3

3. The CRITICAL values of the inequality are -4 and 3
Plot -4 and 3 on a number line with CLOSED dots (Closed not open since the inequality is “greater than and equal to” -3 -4 -5 -6 1 2 3 4 5 6 -1 -2
The two critical values split the number line into three intervals. To determine which intervals satisfy the inequality test a value of x inbetween the two dots.
x = 0; = 0
≥ 12 (does not satisfy)
Since the inequality isn’t satisfied between x = -4 and x =3
The solution is x ≤ -4 and x ≥ 3

4. Solve x2 - 11x + 24 < 0 x2 - 11x + 24 = 0 (x – 3)(x – 8) = 0
x = 3 or x = 8 (critical values)
Open dots since it is not “equal to” 3 4 5 6 7 8 9 2 1
The solution is 3 < x < 8
x = 5; – 11(5) + 24 = -6
< 0 (does satisfy)

5. Classwork and Homework
Solve:
x2 – 5x – 14 > 0
x2 + 3x – 4 < 0
x2 – x – 2 ≤ 0