-19x - 34 = 56 - x

Get rid of all terms on the LEFT which DO NOT contain x

The -34 on the LEFT DOES NOT contain x, so we get rid 
of it by adding its opposite, +34 to both sides

           -19x - 34 = 56 - x
                 +34  +34
         ----------------------
           -19x      = 90 - x

Get rid of all terms on the RIGHT which DO contain x        

The -x on the RIGHT DOES contain x, so we get rid 
of it by adding its opposite, +x to both sides

           -19x      = 90 - x
             +x            +x
         ----------------------
           -18x      = 90

Now we divide both sides by the coefficient of x, 
which is -18

           -18x           90
          ------     =  -----
           -18           -18

Dividing on the left gives just x; dividing on 
the right gives -5, so we have

              x      =  -5 

That's the answer. To check it we replace x 
by (-5) in the original equation:

                     ?
           -19x - 34 = 56 - x
                   
                     ?
        -19(-5) - 34 = 56 - (-5)

                     ? 
             95 - 34 = 56 + 5

                     Ö 
                  61 = 61 
        
Both sides have the same number, 61, so the 
solution, -5, is correct.

Edwin