Question

How do you solve `\frac { 6} { 2x - 1} = \frac { 1} { x - 8}`?

Answer 1

`x=11.75`

Explanation:

Firstly, we should at least try to get a common denominator because we know that both are the fractions are the same. We just have to get the common denominator to make everything easier for us.

Now, we multiply the left side by `x-8` on the top and bottom. (Bottom we really don't care about). The top should be `6x-48` (since we multiplied it by x-8).

The right side should be multiplied by `2x-1` to get `2x-1` on the top. We now solve for x by making them equal each other.

`6x-48=2x-1`.
Add 48 to both sides, subtract 2x on both sides to get...

`4x=47`

`x=47/4` or 11.75

You can plug it into the original so they can equal each other.

-Sakuya