Absolute Value Equations 2

harpazo

Pure Mathematics
Let's go back to high school together as we explore the world of absolute value equations. Ready to have fun with math?

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Jason

Well-known member
[math]| x - 10| = 100 [/math]
[math](x - 10) = 100 [/math]
[math]x - 10 = 100 [/math]
[math]x - 10 + 10 = 100 + 10[/math]
[math]x = 110[/math]
Check

[math]|(110) - 10| = 100[/math]
[math]|100| = 100[/math]
Negative side:

[math]| x - 10| = 100 [/math]
[math]-(x - 10) = 100 [/math]
[math]-x + 10 = 100 [/math]
[math]-x + 10 - 10 = 100 - 10 [/math]
[math]-x = 90[/math]
[math]\dfrac{x}{-1} = \dfrac{90}{-1}[/math]
[math]x = -90[/math]
Check

[math]|(-90) - 10| = 100[/math]
[math]|-100| = 100[/math]
Two solutions of [math]110,-90[/math]
 

harpazo

Pure Mathematics
[math]| x - 10| = 100 [/math]
[math](x - 10) = 100 [/math]
[math]x - 10 = 100 [/math]
[math]x - 10 + 10 = 100 + 10[/math]
[math]x = 110[/math]
Check

[math]|(110) - 10| = 100[/math]
[math]|100| = 100[/math]
Negative side:

[math]| x - 10| = 100 [/math]
[math]-(x - 10) = 100 [/math]
[math]-x + 10 = 100 [/math]
[math]-x + 10 - 10 = 100 - 10 [/math]
[math]-x = 90[/math]
[math]\dfrac{x}{-1} = \dfrac{90}{-1}[/math]
[math]x = -90[/math]
Check

[math]|(-90) - 10| = 100[/math]
[math]|-100| = 100[/math]
Two solutions of [math]110,-90[/math]

Hope you like your journey back to Algebra 1.
 
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