What is the solution to |x-10|=3x-2?

Question

anonymous · Answer

But don't I have to make them two separate equations or something, that's what confuses me?

anonymous · Answer

if $x>10$ then $$|x-10|=x-10$$ solve 
$$x-10=3x-2$$

anonymous · Answer

you get 
$$-10=2x-2\
-12=2x\
x=-6$$ but this is NOT a solution because we were assuming that $x>10$ and $-6$ is less than $10$

anonymous · Answer

oh i made a mistake doh

anonymous · Answer

$$x-10=3x-2\
-10=2x-2\
-8=2x\
x=-4$$ still NOT A SOLUTION

anonymous · Answer

then if $x<10$ you have $|x-10|=10-x$ solve 
$$10-x=3x-2$$

anonymous · Answer

$$10-x=3x-2\
10=4x-2\
12=4x\
x=3$$

anonymous · Answer

I'm really lost sorry I just don't understand what you're doing?

anonymous · Answer

and that IS  a solution since $3<10$

anonymous · Answer

lets go slow

anonymous · Answer

you have to get rid of the absolute values when you solve this equation

anonymous · Answer

in order to do that, you have to know whether $$x-10$$ is positive or negative
if $x-10$ is positive, then $|x-10|=x-10$
is that much clear?

anonymous · Answer

Wait so what are the two equations?

anonymous · Answer

we are not there yet
the two equations to solve are 
$$x-10=3x-2$$ or 
$$-(x-10)=3x-2$$ but we have to know something else first

anonymous · Answer

(after consulting my algebra book)
 | x-10 | = 3x-2
x+10>3x-2                
-x      -x
10>2x-2
+2      +2
12/2>2x/2
6>x

anonymous · Answer

@BewaretheDragon this is not an inequality

anonymous · Answer

and that answer is wrong in any case

anonymous · Answer

Okay so what else do I need to know?