First, multiply each side of the equation by #color(red)(70)# to eliminate the fractions while keeping the equation balanced. #color(red)(70)# is the lowest common denominator of the three fractions and eliminating the fractions will make the problem easier to work with.
#color(red)(70)(-3/5 + 1/2w) = color(red)(70) xx -4/7#
#(color(red)(70) xx -3/5) + (color(red)(70) xx 1/2w) = cancel(color(red)(70))10 xx -4/color(red)(cancel(color(black)(7)))#
#(cancel(color(red)(70))14 xx -3/color(red)(cancel(color(black)(5)))) + (cancel(color(red)(70))35 xx 1/color(red)(cancel(color(black)(2)))w) = -40#
#-42 + 35w = -40#
Next, add #color(red)(42)# to each side of the equation to isolate the #w# term while keeping the equation balanced:
#-42 + 35w + color(red)(42) = -40 + color(red)(42)#
#-42 + color(red)(42) + 35w = 2#
#0 + 35w = 2#
#35w = 2#
Now, divide each side of the equation by #color(red)(35)# to solve for #w# while keeping the equation balanced:
#(35w)/color(red)(35) = 2/color(red)(35)#
#(color(red)(cancel(color(black)(35)))w)/cancel(color(red)(35)) = 2/35#
#w = 2/35#
