Download Solving Absolute Value Equations

Solving Absolute Value Equations
• The absolute value of x is defined as
 x, if x  0
x 
 x, if x  0
• Example 1
8    8  8
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 x, if x  0
x 
 x, if x  0
• Example 2
7 7
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• Example 3
x 4
Solve:
Since
4 4
the solution is
and
4  4
x  4, 4
or x  4
The process used above leads to our method
for solving absolute value equations.
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• To solve the absolute value equation
expression  b
1) Write
expression  b
expression  b
2) Solve the resulting equations.
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• Example 4
Solve:
2 x  7  3  2
First, add 3 to both sides
to get the equation in the
form of
expression  b
2x  7  1
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2x  7  1
Write the two equations and solve each.
2x  7  1
2x  7  1
2x  6
2x  8
x3
x4
x  3, 4
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• Example 5
Now solve the same problem again, only this time
use the graphing method.
2 x  7  3  2
Move all terms to the
left hand side.
2x  7  3  2  0
y1
Let y1 equal the left
hand side.
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2x  7  3  2  0
Enter the expression for
y1 into the calculator
Press Zoom-6 to graph
Use Trace to find the
x-intercepts
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y1
Press Trace and then enter 3.
Since the y-value is 0, (3,0) is an x-intercept, and 3 is a
solution to the equation.
Now repeat the process with x = 4, the intercept on the
right.
Again, the y-value is 0.
The solutions to the
equation are x = 3,4
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