# I dont get it

• Aug 2nd 2010, 07:15 PM
Gordon
I dont get it
1. Solve: 2 5 1 - - - = -
3 6 x

Solution:
The LCM of all denominators is
6x. Multiply each side of the
equation by 6x.

6x((2/3) - (5/6)) = 6x(1/x)

Use the distributive law of multi-
plication, which says a(b + c) =
ab + ac
, to rewrite the
equation.

6x(2/3) - 6x(5/6) = 6x(1/x)

Multiply each group of terms
together.

(12x/3) - 30x/6 = 6x/x

Perform each of the indicated
divisions.

4x - 5x = 6

Solve for x.
Combine like terms.

-x = 6

Multiply each side by -1.

x = -6

Why would you Mutliply by 6X rather than just 6?
• Aug 2nd 2010, 07:18 PM
pickslides
Quote:

Originally Posted by Gordon
[B]1. Solve: 2 5 1 - - - = -
3 6 x

• Aug 2nd 2010, 08:32 PM
Soroban
Hello, Gordon!

Doesn't anyone ever PREVIEW their posts?

Quote:

1. Solve: .$\displaystyle \dfrac{2}{3} - \dfrac{5}{6} \;=\;\dfrac{1}{x}$

If you multiply through by $\displaystyle 6$ (only), you get:

. . $\displaystyle 6\,\bigg[\dfrac{2}{3} - \dfrac{5}{6} \;=\;\dfrac{1}{x}\bigg] \quad\Rightarrow\quad 4 - 5 \;=\;\dfrac{6}{x}$

Now what?

• Aug 3rd 2010, 08:11 AM
Gordon
Yeah sorry about that, so So. Why do you mutliply by 6X in the first place that's part i don't get.
• Aug 3rd 2010, 08:21 AM
eumyang
Quote:

Originally Posted by Gordon
Yeah sorry about that, so So. Why do you mutliply by 6X in the first place that's part i don't get.

$\displaystyle 6\bigg[\dfrac{2}{3} - \dfrac{5}{6} \;=\;\dfrac{1}{x}\bigg] \quad\Rightarrow\quad 4 - 5 \;=\;\dfrac{6}{x}$
If you multiply by only 6, you will still have a fraction, with an x in the denominator. Now, the problem was to solve for x. You want to manipulate this equation so that you end with x = some number. It's a little more difficult to solve for x if it's in the denominator, isn't it?
• Aug 3rd 2010, 03:39 PM
Gordon
Yes, i saw his post, but the thing if i were to solve a problem i dont know if i would put an X with whatever number i got, for instant can you give me a problem simliar like that? and i'll try to solve it
• Aug 3rd 2010, 04:06 PM
Quote:

Originally Posted by Gordon
Yes, i saw his post, but the thing if i were to solve a problem i dont know if i would put an X with whatever number i got, for instant can you give me a problem simliar like that? and i'll try to solve it

Hi Gordon,

other problems like this will require the same technique or a more complex variation.
You should stay with it until you've got it...

$\displaystyle \frac{2}{3}-\frac{5}{6}=\frac{1}{x}$

You want to find the value of x, but it's in the denominator position.
That's inconvenient,

but $\displaystyle \frac{x}{x}=1$

Both sides are equal, so if we multiply both sides by the same value,
they will still be equal.
Therefore multiply both sides by x
since then we have an x no longer in the denominator position.

Also multiply both sides by 6 to get rid of all fractions.
Makes things much clearer as far as x is concerned.

$\displaystyle x\left(\frac{2}{3}-\frac{5}{6}\right)=\frac{x}{x}=1$

$\displaystyle x6\left(\frac{2}{3}-\frac{5}{6}\right)=6$

$\displaystyle x\left(6\frac{2}{3}-6\frac{5}{6}\right)=6$

$\displaystyle x(4-5)=6$

$\displaystyle x(-1)=6$

$\displaystyle x=\frac{6}{-1}=-6$
• Aug 3rd 2010, 04:18 PM
Wilmer
Why not keep it simple:

2/3 - 5/6 = 4/6 - 5/6 = -1/6

So 1/x = -1/6 : x = -6
• Aug 3rd 2010, 04:30 PM
Quote:

Originally Posted by Wilmer
Why not keep it simple:

2/3 - 5/6 = 4/6 - 5/6 = -1/6

So 1/x = -1/6 : x = -6

cos the question was

"why would you multiply by 6x rather than just 6"

Anyway, I guess it's your round, Wilmer.
I'll have a pint of Guinness, 2 mars bars and a Havana cigar. Thanks!!
(Beer)(Smoke)(Drunk)
• Aug 3rd 2010, 05:59 PM
Wilmer
Quote:

cos the question was
"why would you multiply by 6x rather than just 6"

Wilmer: my way, multiplying as above is eliminated: so question would not be asked!

Anyway, I guess it's your round, Wilmer.
I'll have a pint of Guinness, 2 mars bars and a Havana cigar. Thanks!!

Wilmer: I'll drink to that !! (and to that, and to that....)
Mars bars with beer? YUK! Pickled wieners much better...

.
• Aug 4th 2010, 07:49 AM
Gordon
Thanks Archie, at first i couldn't get it, but after Wil. show me the simple way and i certain that i fully understand now so thanks to both of you