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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 . 0. 3. 12. 5.4. 5. -7. -16. 10. -23. Opposites vs. Absolute Value. Given Number.
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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 0 3 12 5.4 5 -7 -16 10 -23
Opposites vs. Absolute Value Given Number Opposite Absolute Value 8 - 8 -24 +24 -3.5 +3.5
Solve each equation below. 1) 4) “no solution” x = 10 or -10 2) 5) x = 14 or - 14 x = 4 or - 4 3) 6) x = 0 3 3 t = or - 4 4
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:
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