How do you solve $abs(-2x+4)=6$ ?

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Answer 1 · 2015-04-03T18:24:34

There are 2 possibilities $x<2$ and $x>2$ (we can ignore the possible third possibility $x=2$ by inspection).

If $x<2$ then $(-2x+4)$ is positive and
$abs(-2x+4) = (-2x+4)$
In which case
$-2x+4 = 6$
$x=-1$

If $x>2$ then $(-2x+4)$ is negative and
$abs(-2x+4) = 2x-4$
in which case
$2x-4 = 6$
$x=5$

$x=-1$
or
$x=5$

How do you solve abs(-2x+4)=6abs(-2x+4)=6?