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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
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
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 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.
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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