Solving Equations Examples And Worksheet Page 10
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14A58
Appendix A
Review of Fundamental Concepts of Algebra
Equations with Absolute Values
To solve an equation involving an absolute value, remember that the expression inside
the absolute value signs can be positive or negative. This results in two separate
equations, each of which must be solved. For instance, the equation
x
2
3
results in the two equations
x
2
3
and
x
2
3,
which implies that the equa-
tion has two solutions:
x
5
and
x
1.
Example 14
Solving an Equation Involving Absolute Value
2
Solve
x
3x
4x
6.
Solution
Because the variable expression inside the absolute value signs can be positive or
negative, you must solve the following two equations.
First Equation
2
x
3x
4x
6
Use positive expression.
2
x
x
6
0
Write in general form.
x
3 x
2
0
Factor.
x
3
0
x
3
Set 1st factor equal to 0.
x
2
0
x
2
Set 2nd factor equal to 0.
Second Equation
2
x
3x
4x
6
Use negative expression.
2
x
7x
6
0
Write in general form.
x
1 x
6
0
Factor.
x
1
0
x
1
Set 1st factor equal to 0.
x
6
0
x
6
Set 2nd factor equal to 0.
Check
?
2
3
3
3
4
3
6
Substitute
3
for
x.
✓
18
18
3
checks.
?
2
2
3
2
4
2
6
Substitute 2 for
x.
2
2
2 does not check.
?
2
1
3
1
4
1
6
Substitute 1 for
x.
✓
2
2
1 checks.
?
2
6
3
6
4
6
6
Substitute 6 for
x.
18
18
6 does not check.
The solutions are
x
3
and
x
1.
Now try Exercise 151.
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