Answer
If the inequality symbol were $\geq$, the solution would be all real numbers because the inequality would simplify to $-6\geq-6$, which is always true.
Work Step by Step
Solve the inequality.
$-2(3-x)\gt 2x-6$ $\longrightarrow$ multiply using the distributive property
$-6+2x\gt2x-6$ $\longrightarrow$ subtract 2x from both sides
$-6+2x-2x\gt2x-6-2x$ $\longrightarrow$ combine like terms
$-6\gt-6$
Since the above is not true, the inequality has no solution.
