First, multiply each side of the equation by color(red)(24)24 to eliminate the fractions. color(red)(24)24 is the lowest common denominator of the three fractions and eliminating the fractions will make the problem easier to work:
color(red)(24)(5/8x - 1/3) = color(red)(24)(2x - 5/6)24(58x−13)=24(2x−56)
(color(red)(24) xx 5/8x) - (color(red)(24) xx 1/3) = (color(red)(24) xx 2x) - (color(red)(24) xx 5/6)(24×58x)−(24×13)=(24×2x)−(24×56)
(cancel(color(red)(24))3 xx 5/color(red)(cancel(color(black)(8)))x) - (cancel(color(red)(24))8 xx 1/color(red)(cancel(color(black)(3)))) = 48x - (cancel(color(red)(24))4 xx 5/color(red)(cancel(color(black)(6))))
15x - 8 = 48x - 20
Next, subtract color(red)(15x) and add color(blue)(20) to each side of the equation to isolate the x term while keeping the equation balanced:
15x - 8 - color(red)(15x) + color(blue)(20) = 48x - 20 - color(red)(15x) + color(blue)(20)
15x - color(red)(15x) - 8 + color(blue)(20) = 48x - color(red)(15x) - 20 + color(blue)(20)
0 + 12 = 33x - 0
12 = 33x
Now, divide each side of the equation by color(red)(33) to solve for x while keeping the equation balanced:
12/color(red)(33) = (33x)/color(red)(33)
(3 xx 4)/color(red)(3 xx 11) = (color(red)(cancel(color(black)(33)))x)/cancel(color(red)(33))
(color(red)(cancel(color(black)(3))) xx 4)/color(red)(cancel(3) xx 11) = x
4/11 = x
x = 4/11
