Solve the following equation, and check the solution \[ 7-x=-2 x-8 \]

Step 1 ：Start by simplifying the equation by moving all terms involving x to one side and the constants to the other side. This will give us a simpler equation of the form ax = b, where a and b are constants.

Step 2 ：The simplified equation is \(x = -15\).

Step 3 ：Check the solution by substitifying it back into the original equation to ensure it holds true.

Step 4 ：The solution to the equation is \(\boxed{-15}\).