To solve for #w#, do the same actions to both sides of the equals sign.
In this case, first, subtract #26# from both sides of the equation. Then, multiply by #-1#. Here's the problem with the steps written on the side (I put any multiplying or subtracting in blue):
#color(white){color(black)(
(-w+26=200, qquadqquad "The original equation"),
(-w+26color(blue)(-26)=200color(blue)(-26), qquadqquad "Subtract "26" from both sides of the equals sign"),
(-w+color(red)cancel(color(black)(26-26))=200-26, qquadqquad 26-26" is just "0),
(-w+0=200-26, qquadqquad "Rewrite the above step"),
(-w=200-26, qquadqquad -w+0" is just "-w),
(-w=174, qquadqquad 200-26" is "174),
(-wcolor(blue)(xx-1)=174color(blue)(xx-1), qquadqquad"Multiply both sides of the equals sign by "-1),
(w=174xx-1, qquadqquad -wxx-1" is just "w),
(w=-174, qquadqquad 174xx-1" is "-174)
:}#
The answer is #w=-174#. We can verify this answer by plugging it back in to the original problem. If it returns a true statement (like #1=1# or #-5=-5#), then we know our answer is correct.
#color(white)=>-w+26=200#
#=>-(-174)+26=200#
#color(white)=>174+26=200#
#color(white)=>200=200#
Since this statement is true, our answer is correct.
