Post on 18-Jan-2018
description
Solving Absolute Value Equations
, if 0, if 0
x xx
x x
• The absolute value of x is defined as
• Example 1
8 8 8
, if 0, if 0
x xx
x x
• Example 2
7 7
• Example 3
4x Solve:
Since 4 4 and 4 4
the solution is
or4,4
4xx
The process used above leads to our method for solving absolute value equations.
• To solve the absolute value equation
1) Write
2) Solve the resulting equations.
expression b
expression b expression b
• Example 4
Solve: 2 7 3 2x
First, add 3 to both sides to get the equation in the form of
expression b
2 7 1x
Write the two equations and solve each.
2 7 1x
2 7 1x 2 7 1x
2 6x
3x
2 8x
4x
3,4x
• Example 5
Now solve the same problem again, only this time use the graphing method.
2 7 3 2x
Move all terms to the left hand side.
2 7 3 2 0x
Let y1 equal the left hand side.
1y
2 7 3 2 0x
Enter the expression for y1 into the calculator
1y
Press Zoom-6 to graph
Use Trace to find the x-intercepts
Press Trace and then enter 3.
Now repeat the process with x = 4, the intercept on the right.
Since the y-value is 0, (3,0) is an x-intercept, and 3 is a solution to the equation.
Again, the y-value is 0.
The solutions to the equation are x = 3,4