# How do you solve \frac { 6w - 2} { 5} - \frac { 5w - 4} { 6} = 1?

Mar 3, 2017

$w = 2$

#### Explanation:

$\frac{6 w - 2}{5} - \frac{5 w - 4}{6} = 1$

Get common denominators by multiplying the first term by $\frac{6}{6}$ and the second by $\frac{5}{5}$. Notice that this doesn't change the value of the expression since we are essentially multiplying by $1$.

$\frac{6}{6} \cdot \frac{6 w - 2}{5} - \frac{5}{5} \cdot \frac{5 w - 4}{6} = 1$

$\frac{36 w - 12}{30} - \frac{25 w - 20}{30} = 1$

$\frac{36 w - 12 - \left(25 w - 20\right)}{30} = 1$

$\frac{36 w - 12 - 25 w + 20}{30} = 1$

$36 w - 12 - 25 w + 20 = 30$

$11 w + 8 = 30$

$11 w = 22$

$w = 2$