Question

How do you solve `\frac { 5} { 6} x + \frac { 1} { 2} = \frac { 1} { 4} ( x - 4)`?

Answer 1

See the entire solution process below:

Explanation:

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

`color(red)(12)(5/6x + 1/2) = color(red)(12) xx 1/4(x - 4)`

`(color(red)(12) xx 5/6x) + (color(red)(12) xx 1/2) = cancel(color(red)(12)) 3 xx 1/color(red)(cancel(color(black)(4)))(x - 4)`

`(cancel(color(red)(12)) 2 xx 5/color(red)(cancel(color(black)(6)))x) + (cancel(color(red)(12)) 6 xx 1/color(red)(cancel(color(black)(2)))) = 3(x - 4)`

`10x + 6 = 3(x - 4)`

Then, expand the terms within parenthesis on the right side of the equation:

`10x + 6 = (3 xx x) - (3 xx 4)`

`10x + 6 = 3x - 12`

Next, subtract `color(red)(3x)` and `color(blue)(6)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`10x + 6 - color(red)(3x) - color(blue)(6) = 3x - 12 - color(red)(3x) - color(blue)(6)`

`10x - color(red)(3x) + 6 - color(blue)(6) = 3x - color(red)(3x) - 12 - color(blue)(6)`

`7x + 0 = 0 - 18`

`7x = -18`

Now, divide each side of the equation by `color(red)(7)` to solve for `x` while keeping the equation balanced:

`(7x)/color(red)(7) = -18/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = -18/7`

`x = -18/7`