# How do you solve the equation 2/7k-1/14k=-3?

Mar 29, 2018

Raise all fractional coefficients to the lowest common denominator and combine to find $k = - 14$

#### Explanation:

The first thing we want to do is make sure both of $k$'s coefficients have the same denominator. Once this is done, we can add the coefficients together:

$\frac{2}{7} k - \frac{1}{14} k = k \left(\frac{2}{7} - \frac{1}{14}\right) = - 3$

$k \left(\frac{2}{7} \cdot \frac{2}{2} - \frac{1}{14}\right) = k \left(\frac{4}{14} - \frac{1}{14}\right) = - 3$

$\frac{3}{14} k = - 3$

Finally, we'll divide through by $k$'s coefficient to find our solution. Remember, when you divide by a fraction, you can simply multiply by its inverse to get the same effect!

$\cancel{\frac{3}{14} \times \frac{14}{3}} k = - \cancel{3} \times \frac{14}{\cancel{3}}$

$\Rightarrow k = - 14$