8.2.2: Solve an Absolute-Value Equation
Examples:
Solve the following equations:
(a)
ǀ
x
–
3
ǀ
= 4
(b)
ǀ
3x
–
2
ǀ
= 4
(c)
ǀ
2
–
3x
ǀ
+ 5 = 10
7

8.2.2: Solve an Absolute-Value Equation
In some applications, there is more than one absolute value
in an equation. Consider an equation of the form
ǀ
x
ǀ
=
ǀ
y
ǀ
Since the absolute values of
x
and
y
are
equal
,
x
and
y
are
the
same distance
from 0, which means they are either
equal
or
opposite
in sign.
Example:
Solve the following equations:
(a)
ǀ
3x
–
4
ǀ
=
ǀ
x
+
2
ǀ
8

8.2: Solving Absolute-Value Inequalities
Objectives:
8.2.1: Solve a compound inequality
8.2.2: Solve an absolute-value inequality
9

8.2.1: Solve a Compound Inequality
A
compound inequality
is the inequality that combines
between two inequalities.
Example of compound inequality is
–
2 < x < 5. It is called a
compound inequality because it combines
–
2 < x and x < 5.
Because there are
two
inequality signs in a single statement,
these are sometimes called
double inequalities
.
Examples:
Solve and graph the following compound inequality
a)
3
≤
2x + 1
≤
7
We find an equivalent statement in which the variable is
isolated in the middle.
b)
2x
–
3 <
–
5
or
2x
–
3 >
5
10

2.8.2: Solve an Absolute-Value Inequality
Imagine you get a call from your friend saying that he is driving
from Al Ain to Dubai. But, his car stuck on the highway within 5

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- Fall '18
- jane
- Accounting, Elementary algebra, Negative and non-negative numbers, Binary relation