First, multiply each side of the equation by #color(red)(15)# to eliminate the fractions and keep the equation balanced:

#color(red)(15)(x - 2/5) = color(red)(15) xx -8/15#

#(color(red)(15) xx x) - (color(red)(15) xx 2/5) = cancel(color(red)(15)) xx -8/color(red)(cancel(color(black)(15)))#

#15x - (cancel(color(red)(15)) 3 xx 2/color(red)(cancel(color(black)(5)))) = -8#

#15x - 6 = -8#

Next, add #color(red)(6)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#15x - 6 + color(red)(6) = -8 + color(red)(6)#

#15x - 0 = -2#

#15x = -2#

Now, divide each side of the equation by #color(red)(15)# to solve for #x# while keeping the equation balanced:

#(15x)/color(red)(15) = -2/color(red)(15)#

#(color(red)(cancel(color(black)(15)))x)/cancel(color(red)(15)) = -2/15#

#x = -2/15#

To validate the solution we need to substitute #color(red)(-2/15)# back into the original equation for #color(red)(x)# and calculate the left side of the equation to ensure it equals #-8/15#:

#color(red)(x) - 2/5 = -8/15# becomes:

#color(red)(-2/15) - 2/5 = -8/15#

#color(red)(-2/15) - (3/3 xx 2/5) = -8/15#

#color(red)(-2/15) - 6/15 = -8/15#

#-8/15 = -8/15# therefore we have checked our solution.