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Absolute Value
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View Full Document A lot of people know that when you take the absolute value of a number the answer is
positive, but do you know why? Let's find out:
The absolute value measures the DISTANCE a number is away from the origin (zero) on
the number line.
No matter if the number is to the left (negative) or right (positive) of zero on
the number line, the DISTANCE it is away from zero is going to be positive. Hence, the absolute
value is always positive (or zero if you are taking the absolute value of 0).
Example 1
: What two numbers have an absolute value of 7?
View a video of this example
If you said 7 and 7, you are correct  good for you.
Now, I want to explain the thought behind it because this is going to help us to understand how
to solve absolute value equations. I really want to emphasize the fact that there are two numbers
that are the same distance away from the origin, the positive number and its opposite. The
thought behind this is there are two places on the number line that are 7 units away from zero 
both 7 and 7.
Solving an Absolute Value Equation
Step 1:
Use the definition of absolute value to set up the equation
without absolute values.
If
d
is POSITIVE and
x = d
, then
x = d OR x = d
(two equations are set up)
If
d
is NEGATIVE and 
x = d,
then
No solution
This is because distance (
d
)
can not be negative.
Step 2:
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This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.
 Spring '11
 Kindle
 Algebra

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