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

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.

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. ( - ∞, ∞ )

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

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

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

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

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

Rational Inequalities Solve 5 + 7x 1 + 2x < 4

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

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