First, add #color(red)(1/3)# to each side of the equation to isolate the #x# terms while keeping the equation balanced:
#(3x)/5 + x - 1/3 + color(red)(1/3) = 2/15 + color(red)(1/3)#
#(3x)/5 + x - 0 = 2/15 + (5/5 xx color(red)(1/3))#
#(3x)/5 + x = 2/15 + (5 xx color(red)(1))/(5 xx color(red)(3))#
#(3x)/5 + x = 2/15 + 5/15#
#(3x)/5 + x = 7/15#
Next, combine like term on the left side of the equation:
#(3x)/5 + 1x = 7/15#
#(3/5 + 1)x = 7/15#
#(3/5 + [5/5 xx 1])x = 7/15#
#(3/5 + 5/5)x = 7/15#
#(3 + 5)/5x = 7/15#
#8/5x = 7/15#
Now, multiply each side of the equation by #color(red)(5)/color(blue)(8)# to solve for #x# while keeping the equation balanced:
#color(red)(5)/color(blue)(8) xx 8/5x = color(red)(5)/color(blue)(8) xx 7/15#
#cancel(color(red)(5))/cancel(color(blue)(8)) xx color(blue)(cancel(color(black)(8)))/color(red)(cancel(color(black)(5)))x = cancel(color(red)(5))/color(blue)(8) xx 7/(color(red)(cancel(color(black)(15)))3)#
#x = color(red)(1)/color(blue)(8) xx 7/3#
#x = (color(red)(1) xx 7)/(color(blue)(8) xx 3)#
#x = 7/24#
