4/x=-20/15 solve for x in the proportion

- anonymous

4/x=-20/15 solve for x in the proportion

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- schrodinger

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- Hero

Hint: Cross Mulitply

- anonymous

cross multiply

- anonymous

ok

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## More answers

- Hero

@shivraj , why don't you post the result you get after cross multiplication.

- anonymous

Here we can do it by another simple method..

- Hero

You mean a method other than cross multiplication?

- anonymous

Yes..

- anonymous

Let @shivraj solve first and at last I will tell the method..

- Hero

Okay, so @waterineyes will probably simplify the right fraction before cross multiplying. But that's nothing new.

- anonymous

I will not use cross multiplication anywhere in my solution @Hero

- Hero

So how will your method be "simpler"?

- anonymous

Can i show you??

- Hero

I can see that the fraction will be reduced to 4x = -4/3

- Hero

But now you still have to cross multiply. Doing anything else will just produce more steps.

- anonymous

I won't i said @Hero

- Hero

err, I mean the fraction will be reduced to 4/x = -4/3 typo above

- anonymous

Yes:
\[\frac{4}{x} = \frac{-4}{3} \implies \frac{4}{x} = \frac{4}{-3} \implies x = -3\]

- Hero

Oh, I see what you did. Yeah, in that case, I guess you don't need to cross multiply. Nice trick.

- anonymous

That is what I am trying to say..

- Hero

That's why the real first step is to actually simplify whenever possible

- anonymous

Yes...

- Hero

Usually when I see a proportion, my first impulse is to cross multiply

- anonymous

Ha ha ha..

- anonymous

@waterineyes : Unknowingly you are cross multiplying the terms with 1. :) Still it's a good and simpler method. Well done.

- anonymous

See the way to look this problem is :
If;
\[\frac{x}{y} = \frac{x}{z}\]
then y must be equal to z that is why they become equal..
That is the trick here.. @Champs

- anonymous

You are of course saying it mathematically but I am saying it logically...

- Hero

What do you call that? The Denominator Equivalency Property?

- anonymous

Ha ha ha..
You can call that what you like..

- Hero

Or perhaps the Denominator Equality Property

- anonymous

I like it. :)

- Compassionate

We see in this Problem that when a single fraction is equal to a single fraction, then the equation can be cleared by "cross-multiplying."
If
a c
---- = ----
b d
,
then
ad = bc.
--------------------------------------------------------
PROBLEM BELOW
--------------------------------------------------------
x − 3 x − 5
------ = ----- <=== SOLVE
3 2
Here is the cleared equation and its solution:
2(x − 3) = 3(x − 5)
2x − 6 = 3x − 15
2x − 3x = − 15 + 6
−x = −9
x = 9

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