Pre-Calculus

Section P.2Solving Inequalities

IntroductionGraphs 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 1Write 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 InequalitiesEx. 2: Solve the inequality and write the solution

interval. 8x – 4 < 4x + 12

Double InequalitiesEx 3: Solve the inequality and write the solution

interval .

-9 ≤ 7x – 2 < 12

Inequalities Using Absolute ValuesExample 4: Solve the inequalities. Less than “and”, greater than “or”

| x - 13 | < 7 | x + 3 | ≥ 8

Polynomial InequalitiesSolveFind critical values, test the intervals. x2 – 2x – 8 < 0

Rational InequalitiesSolve 5 + 7x 1 + 2x < 4

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

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