First, multiply each side of the equation by #color(red)(15)# to eliminate the fractions while keeping the equation balanced. We multiply by #color(red)(15)# because it is the LCD (Lowest Common Denominator) of all the fractions:
#color(red)(15)(-1/5w + 2/3) = color(red)(15)(-7/3w - 3)#
#(color(red)(15) xx -1/5w) + (color(red)(15) xx 2/3) = (color(red)(15) xx -7/3w) - (color(red)(15) xx 3)#
#(cancel(color(red)(15))3 xx -1/color(red)(cancel(color(black)(5)))w) + (cancel(color(red)(15))5 xx 2/color(red)(cancel(color(black)(3)))) =(cancel(color(red)(15))5 xx -7/color(red)(cancel(color(black)(3)))w) - 45#
#-3w + 10 = -35w - 45#
Next, subtract #color(red)(10)# and add #color(blue)(35w)# to each side of the equation to isolate the #w# term while keeping the equation balanced:
#-3w + 10 - color(red)(10) + color(blue)(35w) = -35w - 45 - color(red)(10) + color(blue)(35w)#
#-3w + color(blue)(35w) + 10 - color(red)(10) = -35w + color(blue)(35w) - 45 - color(red)(10)#
#(-3 + color(blue)(35))w + 0 = 0 - 55#
#32w = -55#
Now, divide each side of the equation by #color(red)(32)# to solve for #w# while keeping the equation balanced:
#(32w)/color(red)(32) = -55/color(red)(32)#
#(color(red)(cancel(color(black)(32)))w)/cancel(color(red)(32)) = -55/32#
#w = -55/32#
