Objective- To solve problems involving absolute value of numbers or variables. Absolute value- A numbers distance from zero on the number line. -5 -4 -3 -2 -1 0 1 2 3 4 5 3 12 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

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? -50 ft./sec. B) What is its speed? +50 ft./sec.

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:

False, x = 0 True False, x = -7 True False, x = -5 True 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) 4) False, x = 0 True 2) 5) False, x = -7 True 3) 6) False, x = -5 True