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

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

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

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|? _________

Absolute value: The distance from zero on the number line

Opposites vs. Absolute Value Given NumberOppositeAbsolute Value

t = or 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

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

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.

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:

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