Help me with absolute values, textbook doesn't explain question all the way .

[hgncommand]

Okay, so an absolute value of

|x - 5| = |3x+7|

I have one solution which is

x - 5 = 3x + 7
v
-5 = 2x + 7 - 7
-12 = 2x
-6 = x

And the other (absolute values can be positive or negative)

-x + 5 = -3x - 7
-x + 5 - 5 = -3x - 7 -5
-x = -3x + 3x - 12
2x = -12
x -6

Are there 4 solutions since there are 2 absolute values? If so, how do I go about doing that?
Thanks to all the math whizzes who are going to help me out.

Edit: Answers are defined as -6 and -1/2

[sbradford26]

So what are you asking?

[professor cool.]

theres only two solutions

[editline]18th November 2010[/editline]

also, do your own homework

[rawr >:3]

absolute value of a negative number, IE -6, is 6. so |-6|=6

[sbradford26]

[QUOTE=rawr >:3;26148489]absolute value of a negative number, IE -6, is 6. so |-6|=6[/QUOTE]

That about sums it up.

[hgncommand]

I assumed that, but the textbook lists -1/2 as another solution, which threw me off.

[professor cool.]

[QUOTE=hgncommand;26148762]I assumed that, but the textbook lists -1/2 as another solution, which threw me off.[/QUOTE]

|x-5| = |3x+7|
-x+5 = 3x+7
5 = 4x+7
-2=4x

maybe? im not very good at math, that's probably wrong. but it does come out to -1/2

[hgncommand]

Yeah, I just did that question at school with a buddy to help me, and I got that, thanks cool.

[Crimson_Bomb]

This thread makes me feel uneducated.

[shatteredwindow]

Absolute value is the distance it is from zero. So basically, just figure out each side normally, but it would have to be positive.

[shatteredwindow]

x^2 -10x +25 = 9x^2 +41x + 49

8x^2 + 51x + 24

fuck it, can't be bothered to do the rest.

[VeryNiceGuy]

If a number is in the bars for Absolute Value, it's always positive.

|6 - 10| + |5 - 9|
|-4| + |-4|
4 + 4
8

understand