# How do you solve \frac { x + 2} { 3} = \frac { 4x + 1} { 11}?

May 28, 2017

$x = 19$

#### Explanation:

First, simplify the equation by cross multiplying:

$\frac{x + 2}{3} = \frac{4 x + 1}{11}$

$\left(4 x + 1\right) \cdot 3 = \left(x + 2\right) \cdot 11$

Or if you prefer the long way:

$\frac{x + 2}{3} = \frac{4 x + 1}{11}$

$\frac{x + 2}{\cancel{3}} \cdot \cancel{3} = \frac{4 x + 1}{11} \cdot 3$
$\left(x + 2\right) \cdot 11 = \frac{4 x + 1}{\cancel{11}} \cdot 3 \cdot \cancel{11}$
$\left(4 x + 1\right) \cdot 3 = \left(x + 2\right) \cdot 11$

Then, distribute the coefficients:

$\left(4 x + 1\right) \cdot 3 = \left(x + 2\right) \cdot 11$

$12 x + 3 = 11 x + 22$

$x = 22 - 3 = 19$

$x = 19$