Find f(x)+12 when the input is 8.
FAST

You get all of the 'x's on one side of the equation, and everything else
on the other side.

I'll use your equation to demonstrate.  Please watch closely:

                                                 6x = 5x + 7

Subtract  5x  from each side:        x  = 7 .

Oops.  Ran out of steps.  That's all this one needs.

' 7 ' is the 'solution' to this equation.  That means:  ' 7 ' is the number
that  'x'  must be in order for the equation to be a true statement. 
If  'x'  is any other number but 7, the equation makes a statement
that's false.

Example:  What if we make  'x'  ten ?  Then the equation says

                6 (10)  =  5 (10) + 7

                  60     =   50    + 7

                     60  =  57      HONK !   Not true !    'x' can only be ' 7 ' .