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Absolute Value The distance on the number line from a number to 0 is called the absolute value of that number.The absolute value of a is written a . Since the distance cannot be negative, the absolute value of a number is always nonnegative. The algebraic definition of absolute value follows: a if a 0 For all real numbers a, a a if a 0 Think of a as the “opposite”of a. Copyright © 2004 Pearson Education, Inc. Slide R-1 Evaluating Absolute Values Examples: Evaluate each expression. 2 3 4 Solutions: 2 2 3 3 4 (4) 4 Copyright © 2004 Pearson Education, Inc. Slide R-2 Applications Systolic blood pressure is the maximum pressure produced by each heartbeat. If 120 is considered a normal systolic pressure, Pd = P 120 , where P is the patients normal systolic pressure. A nurse takes the blood pressure of a patient during a tilt table test, and records that the patients systolic pressure is 86. Find Pd for this patient. Solution: Pd P 120 86 120 34 = 34 Copyright © 2004 Pearson Education, Inc. Slide R-3 Properties of Absolute Value Copyright © 2004 Pearson Education, Inc. Slide R-4 Evaluating Absolute Value Expressions Examples: Let x = 7 and y = 5. 2x 4 y Solution: 5 y 4 x xy Solution: 2 x 4 y 2(7) 4(5) 5 y 4 x xy 14 (20) 14 20 6 6 Copyright © 2004 Pearson Education, Inc. 5 5 4 7 7 5 5 5 28 35 25 28 35 3 35 Slide R-5 Distance Between Points on a Number Line If P and Q are points on the number line with coordinates a and b, respectively, then the distance d(P,Q) between them is d P, Q b a or d P, Q a b Example: Find the distance between 3 and 11. Solution: The distance is given by Alternatively, Copyright © 2004 Pearson Education, Inc. 11 3 11 3 14 14. 3 11 14 14. Slide R-6