Absolute value equation

• Dec 4th 2009, 02:40 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

• Dec 4th 2009, 02:51 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

$\displaystyle |3x-9| = |3-3x|$

$\displaystyle 3|x-3| = 3|1-x|$

$\displaystyle |x-3| = |1-x|$

square both sides ...

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

$\displaystyle 8 = 4x$

$\displaystyle 2 = x$
• Dec 4th 2009, 02:52 PM
Bacterius
Because absolute value turns any negative value into its opposite positive value.

With $\displaystyle 2$, it would give :

$\displaystyle |3x - 9| = |3 - 3x|$

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

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

$\displaystyle |-3| = |-3|$

$\displaystyle 3 = 3$

With $\displaystyle 6$, it would give :

$\displaystyle |3x - 9| = |3 - 3x|$

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

$\displaystyle |18 - 9| = |3 - 18|$

$\displaystyle |-9| = |-15|$

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