# Absolute value equation

• December 4th 2009, 03:40 PM
leoslick
Absolute value equation
If I have

|3x-9|=|3-3x|

I do not see how the solution can be = 2

I would think the solution would be = {2,6}

Can someone explain if I am correct or if the given solution was correct, and why? Thanks

• December 4th 2009, 03:51 PM
skeeter
Quote:

Originally Posted by leoslick
If I have

|3x-9|=|3-3x|

I do not see how the solution can be = 2

I would think the solution would be = {2,6}

Can someone explain if I am correct or if the given solution was correct, and why? Thanks

$|3x-9| = |3-3x|$

$3|x-3| = 3|1-x|$

$|x-3| = |1-x|$

square both sides ...

$x^2 - 6x + 9 = 1 - 2x + x^2
$

$8 = 4x$

$2 = x$
• December 4th 2009, 03:52 PM
Bacterius
Because absolute value turns any negative value into its opposite positive value.

With $2$, it would give :

$|3x - 9| = |3 - 3x|$

$|3 \times 2 - 9| = |3 - 3 \times 2|$

$|6 - 9| = |3 - 6|$

$|-3| = |-3|$

$3 = 3$

With $6$, it would give :

$|3x - 9| = |3 - 3x|$

$|3 \times 6 - 9| = |3 - 3 \times 6|$

$|18 - 9| = |3 - 18|$

$|-9| = |-15|$

$9 \neq 15$, so $x = 6$ is not a solution.