# How do you solve (x+1) / 2 + 1 = (x-5) / 3?

Jul 23, 2016

$x = - 19$

#### Explanation:

First, we have $\frac{x + 1}{2} + 1 = \frac{x - 5}{3}$
Simplifying the left hand side, we have,
$\frac{x + 1}{2} + 1$
$\frac{x + 1 + 2}{2}$
$\frac{x + 3}{2}$
So we now have,
$\frac{x + 3}{2} = \frac{x - 5}{3}$
Multiply each side with the divisor from the other side.
$\left(x + 3\right) \cdot 3 = \left(x - 5\right) \cdot 2$
$3 x + 9 = 2 x - 10$
Subtract $2 x$ from both sides
$3 x - 2 x + 9 = 2 x - 2 x - 10$
$x + 9 = - 10$
Subtract $9$ from both sides
$x + 9 - 9 = - 10 - 9$
$x = - 19$