1. Objective- To solve problems involving absolute value of numbers or variables.
Absolute value- A numbers distance from
zero on the number line. 3 12 5 -7
5.4 10
-23
-16

2. Opposites vs. Absolute Value
Given Number
Opposite
Absolute Value 8
- 8
-24
+24
-3.5
+3.5

3. Solve each equation below.1) 4)
x = 10 or -10
“no solution” 2) 5)
x = 4 or - 4
x = 14 or - 14 3) 6)
x = 0 3 3
t = or - 4 4

4. sometimes never always sometimes sometimes always
Determine whether each statement is true always,
sometimes, or never for all real numbers. 1) 4)
sometimes
never 2) 5)
always
sometimes 3) 6)
sometimes
always

5. Velocity vs. Speed
Velocity - Indicates speed and direction.
Speed - The absolute value of velocity.
Example:
A helicopter descends at 50 feet/second.
A) What is its velocity?
-50 ft./sec.
B) What is its speed?
+50 ft./sec.

6. Counterexamples
To prove a statement true, it must be
proven true for all examples - difficult!
Counterexample -
An example that proves
a statement false.
Statement: All pets are furry.
Counterexample: Goldfish.
Statement:
Counterexample:

7. False, x = 0 True False, x = -7 True False, x = -5 True
Determine whether each statement is true or false
for all real numbers. If it is false, find a counter-
example that proves it is false. 1) 4)
False, x = 0
True 2) 5)
False, x = -7
True 3) 6)
False, x = -5
True