# absolute value problem

• Dec 23rd 2009, 07:21 AM
sri340
absolute value problem
Solve: | x - 3 | + | 3 - x | = 12
• Dec 23rd 2009, 07:33 AM
dedust
see what happen to the equation when $x \geq 3$ and $x \leq 3$
• Dec 23rd 2009, 07:46 AM
Quacky
| x - 3 | + | 3 - x | = 12
Either x-3 or 3-x will be positive. The other will be the negative of the other answer.
For example, if x=1,
x-3=-2
3-x=2
You can prove this algebraicly by saying that:
$x-3=y$
$x=3+y$
$x-y=3$
$-y=3-x$

Because you're taking the modulus of the answer, you'll end up with the same number twice.
Eg
|-2| = 2
|2| = 2
so |x-3|=|3-x|

To get an answer of 12,
|x-3|=6 and |3-x|=6
x=9 or x=-3