algebraic equation

[PLAYNOISE]

Hi im stuck on an equation the problem is:
(2x/3) = 10 - (24/x)

once this problem is solved i need to write it in the form y=0 and i dont know what that means...?

 

[Denis]

Hi im stuck on an equation the problem is:
(2x/3) = 10 - (24/x)
once this problem is solved i need to write it in the form y=0 and i dont know what that means...?

2x/3 + 24/x = 10 ; multiply each term by 3x:
2x^2 + 72 = 30x
x^2 - 15x + 36 = 0
OK?

 

[tkhunny]

(2x/3) = 10 - (24/x)
i need to write it in the form y=0

That is a very odd final request. The ONLY variable in the equation is 'x'. What sense does 'y=' make?

(2x/3) = 10 - (24/x)

Multiply by 3. (Why did I pick that?)

3*(2x/3) = 3*[10 - (24/x)]
2x = 30 - (72/x)

Something that will help, that a beginner might miss. Divide by 2

2x/2 = [30 - (72/x)]/2
x = 30/2 - (72/x)/2
x = 15 - (36/x)

It just gave easier numbers. Always be on the lookout for things that will make your life easier.

Multiply by 'x'. WAIT JUST A MINUTE. Can we do that? We don't know what 'x' is, do we? What if x = 0? Won't that be a problem? For now, I'll just discard x be stating in a loud voice, "x CANNOT BE ZERO (0)!" You need to think about why this is so. OK, I feel better. NOW multiply by 'x'. Why did I pick 'x'?

x*x = [15 - (36/x)]*x
x² = 15*x - 36
x² - 15*x + 36 = 0

I think I'll stop there and see what you can do with it. Hint: Factor?