Download 2.2 PPT

Objective:
Find the opposite and the absolute value of a
number.
Definitions

Absolute Value | |
Represents the distance from 0 on a
number line. (always positive)
For example: The absolute value of -2
is 2, which is written as |-2| = 2
Definitions

Solving Absolute Value Problems
Example: Solve |x| = 2
This results in two equations:
x = 2 and x = -2
Definitions

Opposite (+ / -)
The number on the number line that is
the same distance from zero.
For example: The opposite of 4 is -4.
The opposite of -4 is 4.
Try These
0
 What is the opposite of 0? ______
 What is the opposite of 10? _____
-10
0.8
 What is the opposite of -0.8? ______
-½
 What is the opposite of ½? ______
-59.89
 What is the opposite of 59.89? ______
Try These

Evaluate the expressions
0
 |0| ________
 |7| ________
7
4.5
 |-4.5| _______
-2
 -|-2| _________
-0.8
 -|0.8| _________
Absolute value: The distance from
zero on the number line.

-5 -4 -3 -2 -1
0
1 2
3
4
5
1) 3 = 3
4) 12 = 12
7) 0 = 0
2) -5 = 5
5) - 7 = -7
8) -5.4 = 5.4
3) -10 =
10 6) - -23 = -23 9) - 16 = -16
Opposites vs. Absolute Value
Given Number
Opposite
Absolute Value
8
-8
8 =8
-24
24
-24 = 24
-3.5
3.5
-35
. = 35
.
1
4
2
1
-4
2
1
1
4 =4
2
2
Solve each equation below.
1) x = 10
x = 10 or -10
2) x = 4
x = 4 or - 4
3) x = 0
x=0
4) x = -5
“no solution”
5) - x = -14
x = 14 or - 14
3
6) t =
4
3
3
t = 4 or - 4
Determine whether each statement is true always,
sometimes, or never for all real numbers.
1) x = x
sometimes
2) - x £ x
always
3) x > - x
sometimes
4) x < 0
never
5) - x < - x
sometimes
6) x = - x
always