absolute value problem

**sri340** · December 23rd 2009, 06:21 AM

Solve: | x - 3 | + | 3 - x | = 12

**dedust** · December 23rd 2009, 06:33 AM

see what happen to the equation when $x \geq 3$ and $x \leq 3$

**Quacky** · December 23rd 2009, 06:46 AM

| 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

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