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

Apr 2, 2016

$x = - 35$

Explanation:

color(blue)((x-1)/(3)-(x-1)/2=6

First do fractional part. For that find the LCM of $3$ and $6$ which is $6$

So,

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

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

Use distributive property color(brown)(a(b+c)=ab+ac

$\rightarrow \frac{2 x - 2}{6} - \frac{3 x - 3}{6} = 6$

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

Remember to change the signs

$\rightarrow \frac{2 x - 2 - 3 x + 3}{6} = 6$

Collect like terms

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

$\rightarrow - x + 1 = 6 \cdot 6$

$\rightarrow - x + 1 = 36$

$\rightarrow - x = 36 - 1$

$\rightarrow - x = 35$

color(green)(rArrx=-35