How do you solve #2/3x+5/6=7/8x-1/2#?

Question

Julia Adams · Accepted Answer

See the entire solution process below:

First, multiply both sides of the equation by #color(red)(24)# to eliminate the fractions while keeping the equation balanced #color(red)(24)# is the Lowest Common Denominator of the 4 fractions: #color(red)(24)(2/3x + 5/6) = color(red)(24)(7/8x - 1/2)# #(color(red)(24) * 2/3x) + (color(red)(24) * 5/6) = (color(red)(24) * 7/8x) - (color(red)(24) * 1/2)# #(cancel(color(red)(24)) 8 * 2/color(red)(cancel(color(black)(3)))x) + (cancel(color(red)(24)) 4 * 5/color(red)(cancel(color(black)(6)))) = (cancel(color(red)(24)) 3 * 7/color(red)(cancel(color(black)(8)))x) - (cancel(color(red)(24)) 12 * 1/color(red)(cancel(color(black)(2))))# #16x + 20 = 21x - 12# Next, subtract #color(red)(16x)# and add #color(blue)(12)# to each side of the equation to isolate the #x# term while keeping the equation balanced: #-color(red)(16x) + 16x + 20 + color(blue)(12) = -color(red)(16x) + 21x - 12 + color(blue)(12)# #0 + 32 = (-color(red)(16) + 21)x - 0# #32 = 5x# Now, divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced: #32/color(red)(5) = (5x)/color(red)(5)# #32/5 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))# #32/5 = x# #x = 32/5#

Isaiah Anthony · Answer

undefined To solve the equation $ \frac{2}{3}x + \frac{5}{6} = \frac{7}{8}x - \frac{1}{2} $, you first need to eliminate the fractions by finding a common denominator. Once you have a common denominator, you can simplify the equation and solve for $ x $.