# How do you solve \frac { x - 2} { 5} = \frac { 2x - 1} { 11}?

May 15, 2018

$x = 17$

#### Explanation:

Multiply the left-hand numerator $\left(x - 2\right)$ by $11$. Multiply the right-hand numerator $\left(2 x - 1\right)$ by $5$.

So

$11 x - 22 = 10 x - 5$

$11 x - 22 - 10 x = 10 x - 5 - 10 x$

$x - 22 = - 5$

So

$x - 22 + 22 = - 5 + 22$

$x = 17$

You can substitute $17$ in to original equation to check:

$\frac{17 - 2}{5} = \frac{17 \times 2 - 1}{11}$

$3 = 3$