Section 1.8
Absolute Value Equations and Inequalities
Objective 1:
Solving an Absolute Value Equation
The absolute value of a number
x
, written as
x
, represents the
distance
from a number
x
to 0 on the number
line.
Consider the equation
5
x
=
.
To solve for
x
, we must find all values of
x
that are 5 units away from 0 on
the number line.
The two numbers that are 5 units away from 0 on the number line are
5 and
5
x
x
= 
=
as
shown in Figure 8.
5 units from 0
⇓
5 units from 0
⇓
5
0
5
If
5, then
5 or
5
x
x
x
=
= 
=
.
The solution set is
{
}
5,5

.
1.8.2
Solve the equation for
x.
Simplify your answer.
Type an integer or a fraction.
Use a comma to separate
answers as needed.
Objective 2:
Solving an Absolute Value “Less Than” Inequality
The solution to the inequality
5
x
<
consists of all values of
x
whose distance from 0 is less than 5 units on the
number line.
These values are all less than 5 units from 0.
6 4 4 4 4 4 4 447 4 4 4 4 4 4 4 48
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 Spring '09
 moshe
 Algebra, Equations, Inequalities, Elementary algebra, Negative and nonnegative numbers, Inequation

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