Absolute Value

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)