Question

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

Answer 1

`x=-35`

Explanation:

First, we have to compute the common denominator.
The common denominator of the prime numbers `3` and `2` is their product `color(red)6`

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

`rArr(color(red)2(x-1))/color(red)6-(color(red)3(x-1))/color(red)6=6`

`rArr(2(x-1)-3(x-1))/6=6`
`rArr2(x-1)-3(x-1)=6*6` cross multiplication
`rArr2x-2-3x+3=36`
`rArr2x-3x-2+3=36`
`rArr-x+1=36`
`rArr-x=36-1`
`rArr-x=35`
`rArrx=-35`