#color(red)("Using first principles")#
#color(red)("Step 1")#
Have only the terms with #x# in them on the left of the =
Subtract #color(blue)(b)# from both sides
#color(brown)(2x+b" "=" "w" "->" "2x+bcolor(blue)(-b)" "=" "w color(blue)(-b))#
#2x+0=w-b#
#2x=w-b#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(red)("Step 2")#
Have only #x# on the left hand side of the =
Divide both sides by #color(blue)(2)#
#color(brown)(2/(color(blue)(2))xx x=color(blue)(1/2)(w-b)#
#1xx x=1/2(w-b)#
#x=1/2(w-b)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(red)("Comment")#
#1/2(w-b)# is the same as #w/2-b/2#