Answer
$x = 4$
Work Step by Step
$\mid$$2x - 6$$\mid$ $=$ $\mid$$10 - 2x$$\mid$
$2x - 6 = 10 - 2x$
$4x = 16$
$x = 4$
$\mid$$2x - 6$$\mid$ $=$ $\mid$$10 - 2x$$\mid$
$2x - 6 = -10 +2x$
$0 = -4$
$\varnothing$
Therefore, $x = 4$ is the only answer.