SOLUTION: solve the equation. show your steps. (24/2x-8)/(1/x+4)=(13/2)

Question 634996: solve the equation. show your steps.
(24/2x-8)/(1/x+4)=(13/2)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

One way to solve this is...
The equation is a proportion (one fraction equals another fraction). So we can use cross-multiplying:

which simplifies to:

The first fraction reduces:

After all that, we still have a proportion. So we can use cross-multiplying again:

which simplifies to:

The equation now is rather simple to solve. Subtracting 13x from each side:

Subtracting 96 from each side:

Dividing both sides by 11:

During the cross-multiplications we were multiplying by expressions that have been zero (depending on what number x happened to be). It is not wrong to do this. But it does require that you check you answers. You must at lest check to see if any of the denominators are zero. If so, you must reject that solution since we can never divide by zero.

Checking -148/11:

We can now the that the four denominators (, , , ) are all non-zero. (If we had gotten even just one zero denominator we would have to reject this solution. And, since it was the only one we found, there would be no solutions to the equation.)

So our solution passes the required part of the check. You are welcome to finish the check to see if we made a mistake somewhere.
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