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

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- Dec 23rd 2009, 06:21 AMsri340absolute value problem
Solve: | x - 3 | + | 3 - x | = 12

- Dec 23rd 2009, 06:33 AMdedust
see what happen to the equation when $\displaystyle x \geq 3$ and $\displaystyle x \leq 3$

- Dec 23rd 2009, 06:46 AMQuacky
| 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