Question

How do you solve `(x-1) /3 - (x-1)/2 = 6`?

Answer 1

`x = -35`

Explanation:

Start by making sure that you're working with fractions that have equal denominators.

You start with

`(x-1)/3 - (x-1)/2 = 6/1`

The common denominator here is `6`, so multiply the first fraction by `1 = 2/2`, the second fraction by `1 = 3/3`, and the third fraction by `1 = 6/6`.

This will get you

`(x-1)/3 * 2/2 - (x-1)/2 * 3/3 = 6/1 * 6/6`

`(2(x-1))/6 - (3(x-1))/6 = 36/6`

At this point, drop the denominators and focus exclusively on the numerators.

`2(x-1) - 3(x-1) = 36`

This will get you

`-(x-1) = 36`

`-x + 1 = 36`

`x = - 35`

Do a quick check to make sure that the calculations are correct

`(-35 - 1)/3 - (-35 - 1)/2 = 6`

`-36/3 + 36/2 = 6`

`-12 + 18 = 6 " "color(green)(sqrt())`