Question

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

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(12)` to eliminate the fractions while keeping the equation balanced. `color(red)(12)` is the Lowest Common Denominator of the three fractions.

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

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

`(cancel(color(red)(12))4 xx (3x - 1)/color(red)(cancel(color(black)(3)))) + 36/4 = 4(x + 1)`

`4(3x - 1) + 9 = (4 xx x) + (4 xx 1)`

`(4 xx 3x) - (4 xx 1) + 9 = 4x + 4`

`12x - 4 + 9 = 4x + 4`

`12x + 5 = 4x + 4`

Next, subtract `color(red)(5)` and `color(blue)(4x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(blue)(4x) + 12x + 5 - color(red)(5) = -color(blue)(4x) + 4x + 4 - color(red)(5)`

`(-color(blue)(4) + 12)x + 0 = 0 - 1`

`8x = -1`

Now, divide each side of the equation by `color(red)(8)` to solve for `x` while keeping the equation balanced:

`(8x)/color(red)(8) = -1/color(red)(8)`

`(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) = -1/8`

`x = -1/8`