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

Feb 24, 2016

$x = - 35$

#### 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.
$6 \left(\frac{x - 1}{3}\right) - 6 \left(\frac{x - 1}{2}\right) = 6 \left(6\right)$

$2 \left(x - 1\right) - 3 \left(x - 1\right) = 36$

$2 x - 2 - 3 x + 3 = 36$

$- x + 1 = 36$

$- x = 35$

$x = - 35$

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

$\frac{- 35 - 1}{3} - \frac{- 35 - 1}{2} = 6$

$- \frac{36}{3} - - \frac{36}{2} = 6$

$- 12 + 18 = 6$

$6 = 6$