How do you solve #\frac{3}{8}x-\frac{1}{3}=\frac{1}{12}#?

1 Answer
Jan 25, 2018

See a solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(24)# to eliminate the fractions while keeping the equation balanced. We use #color(red)(24)# because it is the Lowest Common Denominator of all the fractions:

#color(red)(24)(3/8x - 1/3) = color(red)(24) xx 1/12#

#(color(red)(24) xx 3/8x) - (color(red)(24) xx 1/3) = cancel(color(red)(24))2 xx 1/color(red)(cancel(color(black)(12)))#

#(cancel(color(red)(24))3 xx 3/color(red)(cancel(color(black)(8)))x) - (cancel(color(red)(24))8 xx 1/color(red)(cancel(color(black)(3)))) = 2#

#9x - 8 = 2#

Next, we can add #color(red)(8)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#9x - 8 + color(red)(8) = 2 + color(red)(8)#

#9x - 0 = 10#

#9x = 10#

Now, we can divide each side of the equation by #color(red)(9)# to solve for #x# while keeping the equation balanced:

#(9x)/color(red)(9) = 10/color(red)(9)#

#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 10/9#

#x = 10/9#