First, multiply each side of the equation by #color(red)(6)# to eliminate the fractions while keeping the equation balanced. #color(red)(6)# is the lowest common denominator of the three fractions:
#color(red)(6)(-5/2y - 3/2) = color(red)(6)(5y - 1/3)#
#(color(red)(6) xx -5/2y) - (color(red)(6) xx 3/2) = (color(red)(6) xx 5y) - (color(red)(6) xx 1/3)#
#(cancel(color(red)(6))3 xx -5/color(red)(cancel(color(black)(2)))y) - (cancel(color(red)(6))3 xx 3/color(red)(cancel(color(black)(2)))) = 30y - (cancel(color(red)(6))2 xx 1/color(red)(cancel(color(black)(3)))) =>#
#-15y - 9 = 30y - 2#
Next, add #color(red)(15y)# and #color(blue)(2)# to each side of the equation to isolate the #y# term while keeping the equation balanced:
#color(red)(15y) - 15y - 9 + color(blue)(2) = color(red)(15y) + 30y - 2 + color(blue)(2)#
#0 - 7 = (color(red)(15) + 30)y - 0#
#-7 = 45y#
Now, divide each side of the equation by #color(red)(45)# to solve for #y# while keeping the equation balanced:
#-7/color(red)(45) = (45y)/color(red)(45)#
#-7/45 = (color(red)(cancel(color(black)(45)))y)/cancel(color(red)(45))#
#-7/45 = y#
#y = -7/45#
