Chapter 2 Section 2 Absolute Value Objective: Find the opposite and the absolute value of a number.

Definitions Absolute Value | | Represents the distance from 0 on a number line. (always positive) For example: The absolute value of -2 is 2, which is written as |-2| = 2

This results in two equations: Definitions Solving Absolute Value Problems Example: Solve |x| = 2 This results in two equations: x = 2 and x = -2

Definitions Opposite (+ / -) The number on the number line that is the same distance from zero. For example: The opposite of 4 is -4. The opposite of -4 is 4.

Try These -10 0.8 -½ -59.89 What is the opposite of 0? ______ What is the opposite of 0? ______ What is the opposite of 10? _____ What is the opposite of -0.8? ______ What is the opposite of ½? ______ What is the opposite of 59.89? ______ -10 0.8 -½ -59.89

Try These 7 4.5 -2 -0.8 Evaluate the expressions |0| ________ |7| ________ |-4.5| _______ -|-2| _________ -|0.8| _________ 7 4.5 -2 -0.8

Absolute value: The distance from zero on the number line. -5 -4 -3 -2 -1 0 1 2 3 4 5 1) 2) 3) 4) 5) 6) 3 12 7) 8) 9) 5 -7 5.4 10 -23 -16

Opposites vs. Absolute Value Given Number Opposite Absolute Value 8 - 8 -24 24 -3.5 3.5

Solve each equation below. 1) 4) x = 10 or -10 “no solution” 2) 5) x = 4 or - 4 x = 14 or - 14 3) 6) x = 0 3 3 t = or - 4 4

sometimes never always sometimes sometimes always Determine whether each statement is true always, sometimes, or never for all real numbers. 1) 4) sometimes never 2) 5) always sometimes 3) 6) sometimes always