Question

How do you solve `\frac { x - 1} { 4} - \frac { x } { 3} = \frac { 1} { 12}`?

Answer 1

See the entire solution below:`x = -4`

Explanation:

First, multiply each side of the equation by `color(red)(12)` to eliminate the fractions while keeping the equation balanced:

`color(red)(12)((x - 1)/4 - x/3) = color(red)(12) xx 1/12`

`(color(red)(12) xx (x - 1)/4) - (color(red)(12) xx x/3) = cancel(color(red)(12)) xx 1/color(red)(cancel(color(black)(12)))`

`(cancel(color(red)(12))3 xx (x - 1)/color(red)(cancel(color(black)(4)))) - (cancel(color(red)(12))4 xx x/color(red)(cancel(color(black)(3)))) = 1`

`3(x - 1) - 4x = 1`

Next, expand the terms in parenthesis:

`(3 xx x) - (3 xx 1) - 4x = 1`

`3x - 3 - 4x = 1`

Then, group and combine like terms on the left side of the equation:

`3x - 4x - 3 = 1`

`(3 - 4)x - 3 = 1`

`-1x - 3 = 1`

Next, add `color(red)(3)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`-1x - 3 + color(red)(3) = 1 + color(red)(3)`

`-1x - 0 = 4`

`-1x = 4`

Now, multiply each side of the equation by `color(red)(-1)` to solve for `x` while keeping the equation balanced:

`color(red)(-1) xx -1x = color(red)(-1) xx 4`

`1x = -4`

`x = -4`