First multiply each side of the equation by #color(red)(20)# to eliminate all of the fractions. #color(red)(20)# is the Lowest Common Denominator for all of the fractions:
#color(red)(20)(2/5 + 1/4) = color(red)(20)(x - 1/2)#
#(color(red)(20) xx 2/5) + (color(red)(20) xx 1/4) = (color(red)(20) xx x) - (color(red)(20) xx 1/2)#
#(cancel(color(red)(20)) 4 xx 2/color(red)(cancel(color(black)(5)))) + (cancel(color(red)(20)) 5 xx 1/color(red)(cancel(color(black)(4)))) = 20x - (cancel(color(red)(20)) 10 xx 1/color(red)(cancel(color(black)(2))))#
#8 + 5 = 20x - 10#
#13 = 20x - 10#
Next, add #color(red)(10)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#13 + color(red)(10) = 20x - 10 + color(red)(10)#
#23 = 20x - 0#
#23 = 20x#
Now, divide each side of the equation by #color(red)(20)# to solve for #x# while keeping the equation balanced:
#23/color(red)(20) = (20x)/color(red)(20)#
#23/20 = (color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20))#
#23/20 = x#
#x = 23/20#
