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
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.