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
