Thread: absolute value problem

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

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

| 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:
$\displaystyle x-3=y$
$\displaystyle x=3+y$
$\displaystyle x-y=3$
$\displaystyle -y=3-x$

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