# Homework Help: Factoring something with absolute value

1. Feb 1, 2010

### zeion

1. The problem statement, all variables and given/known data

I need to find where these intersect:
y = |x|
3y - x = 8

2. Relevant equations

3. The attempt at a solution

I equate them:
|x| = (1/3)x + (8/3)
|x| - (1/3)x - (8/3) = 0
|3x| - x - 8 = 0
|2x| - 8 = 0
|x| = 4

Is that right?
How do I get the other solution?

2. Feb 1, 2010

### Staff: Mentor

The line below is wrong. |3x| - x = 2x if x >=0, but is equal to -4x if x < 0.
Rewrite the line above as
|3x| = x + 8

Now get rid of the absolute values by writing two equations, one for x >= 0 and the other for x < 0. For example, if |a| = 2, then a = 2 or -a = 2.

Look at the section in your book that defines absolute values.

3. Feb 1, 2010

### zeion

Are there some general rules I should know? About when to do a case?

4. Feb 1, 2010

### Staff: Mentor

Just this,
|a| = b ==> a = b or -a = b

5. Feb 1, 2010

### zeion

Okay great thank you I understand now