Question

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

Answer 1

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:

`2/7k-1/14k=k(2/7-1/14)=-3`

`k(2/7*2/2-1/14)=k(4/14-1/14)=-3`

`3/14k=-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(3/14xx14/3)k=-cancel(3)xx14/cancel(3)`

`rArr k=-14`