Question

How do you solve `(x + 1) / 4 = 2 - ( (x + 2) / 5)`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(20)` to eliminate the fractions while keeping the equation balanced:

`color(red)(20)((x + 1)/4) = color(red)(20)(2 - ((x + 2)/5))`

`cancel(color(red)(20))5((x + 1)/color(red)(cancel(color(black)(4)))) = (color(red)(20) xx 2) - (color(red)(20) xx ((x + 2)/5))`

`5(x + 1) = 40 - (cancel(color(red)(20))4 xx ((x + 2)/color(red)(cancel(color(black)(5)))))`

`(5 xx x) + (5 xx 1) = 40 - 4(x + 2)`

`5x + 5 = 40 - (4 xx x) - (4 xx 2)`

`5x + 5 = 40 - 4x - 8`

`5x + 5 = -4x - 8 + 40`

`5x + 5 = -4x + 32`

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

`color(blue)(4x) + 5x + 5 - color(red)(5) = color(blue)(4x) - 4x + 32 - color(red)(5)`

`(color(blue)(4) + 5)x + 0 = 0 + 27`

`9x = 27`

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

`(9x)/color(red)(9) = 27/color(red)(9)`

`(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 3`

`x = 3`