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Section 3-1 Linear Inequalities; Absolute Value Objective: To solve and graph linear inequalities in one variable.

Inequalities All inequalities are in the form a b, a ≤ b, or a ≥ b We solve inequalities similar to solving equations – only ONE DIFFERENCE –When multiply or divide by a negative number, you must flip the sign –Examples: Solve: 3x – 4 ≤ 10 + x Solve:

Inequalities Graphing on the number line –Recall: >, < use open circle ≥, ≤ use closed circle Examples: x ≤ 4 x > < x ≤ 4 -3 < xANDx ≤

Absolute Value Recall: The Absolute Value of a number is the distance from zero to the number –Ex) Both 5 and -5 are 5 units from zero

Absolute Value SentenceMeaningGraphSolution The distance from 0 to x is exactly c units. x = c or x = -c The distance from 0 to x is less than c units. -c < x < c (x -c) The distance from 0 to x is more than c units. x > c or x < -c -cc0 c0 c0 0

SentenceMeaningGraphSolution The distance from x to 5 is 3 units. x = 2 or x = -2 The distance from x to 1 is less than 2 units. -1 < x < 3 The distance from x to -3 is greater than 2 units. x > 1 or x <

Solving Inequalities Algebraically SentenceEquivalent Sentence

Example Solve a) OR 0

AND Example Solve b) 0

Homework p98-99: 3-24 (multiples of three), 25, 26, 27, 30, 33