1. Section P.2 Solving Inequalities
Pre-Calculus
Section P.2
Solving Inequalities

2. Introduction
Graphs of many types of inequalities exist as intervals on the real number line.
Bounded intervals have a finite beginning and end.
Unbounded intervals have an infinite beginning and/or end.

3. Example 1
Write an inequality to represent each interval and state whether the interval is bounded/unbounded and open/closed.
A. (7, 8]
B. (-12, ∞)
C. [ 3, 4]
D. ( - ∞, ∞ )

4. REMEMBER! If you multiply or divide by a negative you must flip the inequality symbol.

5. Linear Inequalities
Ex. 2: Solve the inequality and write the solution interval.
8x – 4 < 4x + 12

6. Double Inequalities
Ex 3: Solve the inequality and write the solution interval .
-9 ≤ 7x – 2 < 12

7. Inequalities Using Absolute Values
Example 4: Solve the inequalities.
Less than “and”, greater than “or”
| x - 13 | < | x + 3 | ≥ 8

8. Polynomial Inequalities
Solve
Find critical values, test the intervals.
x2 – 2x – 8 < 0

9. Rational Inequalities
Solve x
1 + 2x < 4

10. Finding the Domain of a Function
__________
Ex. √(x2 – 5x – 6)

11. Homework
Page 23: every other odd
(1,5,9, 13,…, 141)