Absolute Value Equations

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December 21st 2008, 11:55 AM
magentarita

Absolute Value Equations

It's final exam week. Our teacher is reviewing the material given in class this long semester. However, there are questions that he did not have time to go over but that might be on the final.

Here is a sample:

Solve for x.

|x - 3| = |3x + 2| - 1
December 21st 2008, 12:53 PM
masters

Quote:

Originally Posted by magentarita

It's final exam week. Our teacher is reviewing the material given in class this long semester. However, there are questions that he did not have time to go over but that might be on the final.

Here is a sample:

Solve for x.

|x - 3| = |3x + 2| - 1

Hello Magentarita,

Case 1:

$x-3=(3x+2)-1$

$x=-2$

This solution does not work with the original equation, so throw it out.

Case 2:

$x-3=-(3x+2)-1$

$x=0$

This solution does not work with the original equation, so throw it out.

Case 3:

$-(x-3)=(3x+2)-1$

$\boxed{x=\frac{1}{2}}$

This solution works, so keep it.

Case 4:

$-(x-3)=-(3x+2)-1$

$\boxed{x=-3}$

This solution works, so keep it.
December 21st 2008, 07:06 PM
magentarita

4 cases....

Quote:

Originally Posted by masters

Hello Magentarita,

Case 1:

$x-3=(3x+2)-1$

$x=-2$

This solution does not work with the original equation, so throw it out.

Case 2:

$x-3=-(3x+2)-1$

$x=0$

This solution does not work with the original equation, so throw it out.

Case 3:

$-(x-3)=(3x+2)-1$

$\boxed{x=\frac{1}{2}}$

This solution works, so keep it.

Case 4:

$-(x-3)=-(3x+2)-1$

$\boxed{x=-3}$

This solution works, so keep it.

I had no idea there were 4 cases.

Thanks