The document provides the mathematical definition of absolute value as x if x is positive, 0 if x is 0, and -x if x is negative. It then gives examples of absolute value expressions and their meanings in terms of distance on a number line. It shows how to solve absolute value equations by setting the expression equal to both the positive and negative values. Finally, it lists homework problems from page 55 that include absolute value expressions.

1. September 4, 2009
Warm ­ Up
x, if x is positive
x = { 0,
­x,
if x = 0
if x is negative
Above is the mathematical definition of
absolute value. What is your understanding
of absolute value? How does this match up
with the definition above?

2. x ­ y The distance between
x and y
x ­ 5 = 2 The distance between
x and 5 is 2 units
x + 7 = 5 The distance between
x and ­7 is 5 units

3. Solving Absolute Value
x + 7 = 5
x + 7 = 5 x + 7 = ­5

5. Checking for Extraneous Solutions
2x + 12 = 4x
2x + 12 = 4x 2x + 12 = ­ 4x
12 = 2x 12 = ­ 6x
6 = x ­2 = x
Check: Check:
2(6) + 12 = 4(6) 2(­2) + 12 = 4(­2)

7. HW: pg. 55 #10­38 (1/4), 44­64 (1/4),
83­97 (odd)