Question

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

Answer 1

`x = - 35`

Explanation:

The easiest method to use to solve equations of this form is to use a common denominator, which in this case is 6. Multiply each individual term in the equation by 6 and then simplify the equation and solve for x.
`6( ( x - 1)/3) - 6( ( x - 1 )/2) = 6( 6 )`

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

`2x - 2 -3x + 3 = 36`

`-x + 1 = 36`

`-x = 35`

`x = -35`

Check this answer by substituting -35 in for x in the original equation.

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

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

`-12 + 18 = 6`

`6 = 6`