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

Jun 6, 2016

$x = - 35$

#### Explanation:

$x - 1$ is common to both the terms in the left side of the equation.

Take $x - 1$ and write the remaining terms inside brackets:

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

Now, solve the fractions inside the brackets:

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

$\left(x - 1\right) \left(- \frac{1}{6}\right) = 6$

$- \frac{x - 1}{6} = 6$

Next, multiply both sides by $- 6$:

$- \frac{x - 1}{6} \textcolor{red}{\times - 6} = 6 \textcolor{red}{\times - 6}$

$x - 1 = - 36$

Add $1$ to both sides:

$x - 1 \textcolor{red}{+ 1} = - 36 \textcolor{red}{+ 1}$

$x = - 35$

Let us check our solution

Plug in the value of $x = - 35$ in the given equation and solve:

Left side of the equation is $\frac{x - 1}{3} - \frac{x - 1}{2}$

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

$= \frac{- 36}{3} - \left(- \frac{36}{2}\right)$

$= - 12 - \left(- 18\right)$

$= - 12 + 18$

$= 6 =$ right side of the equation.

Hence, our solution is correct.