The Glade 4.0

I am trying to solve for x

I am looking at [2]/[3]+[4]/[12x] = 5x+[2]/[6x]

I can get the LCD of 12x... giving me

[8x+4]/[12x] + [60x^2+4x]/[12x]

here is where I go fuzzy....
I think I can decrease both sides by 4.... which gives me [2x+1]/[3x] = [15x^2+1x]/[3x]

From there... I think I would want to multiply the whole mess by the 3x... this gives me:
6x^2+3x=45x^3+3x^2

I think from this point I can subtract 3x^2 from both sides leaving 3+3x=45x^3

If I have done things right to this point... I do not know where to go from here. guidance would be greatly appreciated

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Darksiege
Traveller, Calé, Whisperer
Lead me not into temptation; for I know a shortcut

If I'm understanding your original statement correctly:
2/3 + 4/(12x) = 5x + 2/(6x)

I first reduced the fractions:
2/3 + 1/(3x) = 5x + 1/(3x)

Then multiplied both sides of the equation by 3x:
6x/3 + 1 = 15x^2 + 1

Reduced the fraction and dropped the +1 from each side:
2x = 15x^2

Divided each side by x:
2 = 15x

Then divided both sides by 15:
2/15 = x

Does that work, or have I forgotten my Algebra?

_________________
Go back to zero, take a pill, and get well ~ Lemmy Kilmister

You did the right hand side of the equation wrong when you went to consolidate to the LCD. Check the second term in the right-hand numerator again.

And, for God's sake, when you settle on an LCD, just multiply both sides by it to get it out of the way.

As a side note: If you convert everything to an LCD, and then find you can divide out an integer -- you didn't pick the actual LCD, just a CD (not that there's anything technically wrong with that, it just results in bigger numbers that you can cut back down later with extra steps). The LCD in your example is 6x, not 12x, and would have been 3x if you'd simplified the 4/12x term first.

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"Aaaah! Emotions are weird!" - Amdee
"... Mirrorshades prevent the forces of normalcy from realizing that one is crazed and possibly dangerous. They are the symbol of the sun-staring visionary, the biker, the rocker, the policeman, and similar outlaws." - Bruce Sterling, preface to Mirrorshades

Simplifying ASAP is probably your best bet. Not only is it the best time to simplify in almost all cases, but textbooks usually assume you will anyway and the problems just tend to always work out better as a result. Note that simplifying, while it may be required by your teacher, is never a relevant step in a problem -- the algebra will work just fine without it. If you're having problems with a specific math problem, you may try going through it without simplifying at all until the end, just to make sure you aren't making any dumb mistakes* in your simplification.

*which everyone makes, btw... if your teacher does stuff on a black/whiteboard regularly, you will see them make many mistakes in the course of a semester. :p

For this problem, you were more or less doing it right, though with some mistakes that I'm pretty sure will be obvious once you see them. That said, I would start over and just simplify as step #1. Then LCD as you said...

What Kaffis said about multiplying by the LCD once you get one for both sides essentially amounts to just dropping the LCD altogether and is, once again, a case of simplification that isn't strictly necessary but makes the problem look a lot nicer (and will be expected if you continue in math... and if you ever use algebra in real life when you end up actually plugging numbers in for X and such will make your life a lot easier). The way to justify this algebraically is simple enough: since this is an equation, you can do almost anything you want to the equation so long as you do it on both sides. With a LCD of 3x (or 12x as in yours), we can just multiply each side of the equation by 3x (or 12x)... the result for either side is : 3x * [numerator] / 3x. The 3x's will cancel, leaving you with just the numerator on either side.

If the previous paragraph confused you, you can probably just skip it altogether since it isn't strictly necessary and your way works. It just means you'll have to simplify a little later in the problem is all.

In any case, ignoring the minor mistakes, the way you've taken the problem step by step so far is still all correct. You'll want to get all the x's on one side from the step you last left off at. And simplification is likely able to be done at that point again!

Aw, hell. I still made it harder than it had to be.

After simplifying
2/3 + 4/(12x) = 5x + 2/(6x)
to
2/3 + 1/(3x) = 5x + 1/(3x)
I could should have just subtracted 1/(3x) from both sides, leaving
2/3 = 5x
which leaves x = 2/3/5 = 0.1333 (or 2/3 * 1/5 = 2/15 if a fractional answer is what's desired)

_________________
Go back to zero, take a pill, and get well ~ Lemmy Kilmister

[2]/[3]+[4]/[12x] = 5x+[2]/[6x]

(2/3)+(4/12x) = 5x+ (2/6x) or (5x+2)/6x?

_________________
"...but there exists also in the human heart a depraved taste for equality, which impels the weak to attempt to lower the powerful to their own level and reduces men to prefer equality in slavery to inequality with freedom." - De Tocqueville

Multiply everything by X, push it all to one side, quadratic formula.