Solving Absolute Value Equations The absolute value of x is defined as Example 1.
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Transcript of Solving Absolute Value Equations The absolute value of x is defined as Example 1.
![Page 1: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/1.jpg)
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
![Page 2: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/2.jpg)
, if 0, if 0
x xx
x x
• Example 2
7 7
![Page 3: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/3.jpg)
• 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.
![Page 4: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/4.jpg)
• To solve the absolute value equation
1) Write
2) Solve the resulting equations.
expression b
expression b expression b
![Page 5: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/5.jpg)
• 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
![Page 6: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/6.jpg)
Write the two equations and solve each.
2 7 1x
2 7 1x 2 7 1x
2 6x
3x
2 8x
4x
3,4x
![Page 7: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/7.jpg)
• 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
![Page 8: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/8.jpg)
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
![Page 9: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/9.jpg)
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
![Page 10: Solving Absolute Value Equations The absolute value of x is defined as Example 1.](https://reader036.fdocuments.us/reader036/viewer/2022082408/5a4d1b2c7f8b9ab0599993e9/html5/thumbnails/10.jpg)