1. Ch 2.2 Objective: To solve problems involving absolute value of numbers or variables.

2. Definitions Opposite (-) Take the negative of a value to create the opposite of that number. For example: The opposite of 4 is -4. The opposite of -4 is –(-4) = 4. Absolute Value (| |) Represents the distance (which is always positive) from 0 on a number line. For example: The absolute value of -2 is 2 which is written as |-2| = 2 Solving Absolute Value Problems If you remove the absolute value sign, you must replace it with BOTH a positive sign AND a negative sign. For example: Solve |x| = 2 This results in two equations: +x = 2 and –x = 2

3. Try These What is the opposite of 0? ______ What is the opposite of 10? _____ What is the opposite of -6? ______ What is the absolute value of 0 written as |0|? ________ What is the absolute value of 7 written as |7|? ________ What is the absolute value of -5 written as |-5|? _______ What is the opposite of the absolute value of -2 written as -|-2|? _________

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

5. Opposites vs. Absolute Value Given NumberOppositeAbsolute Value 8- 8 -24+24 -3.5+3.5

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

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

8. Velocity vs. Speed Velocity - Indicates speed and direction. Speed - The absolute value of velocity. Example: A helicopter descends at 50 feet/second. A) What is its velocity? B) What is its speed? -50 ft./sec. +50 ft./sec.

9. Counterexamples To prove a statement true, it must be proven true for all examples - difficult! Counterexample -An example that proves a statement false. Statement: All pets are furry. Counterexample: Goldfish. Statement: Counterexample:

10. Determine whether each statement is true or false for all real numbers. If it is false, find a counter- example that proves it is false. 1) 2) 3) 4) 5) 6) False, x = 0 False, x = -7 False, x = -5 True