Question

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

Answer 1

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`