Factoring something with absolute value

[zeion]

Homework Statement

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

Homework Equations

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?

 

[Mark44]

Homework Statement

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

Homework Equations

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

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.

|2x| - 8 = 0
|x| = 4

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

 

[zeion]

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

 

[Mark44]

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

 

[zeion]

Okay great thank you I understand now