# Sipplifying equations with x on both sides and additions

• May 6th 2011, 04:48 AM
NigelS
Sipplifying equations with x on both sides and additions
Hi,

X/1294 = (14851 + X) / 15604

=>

X = 1294 * 14851/ (15604 - 1294)

I can't see how this is done, is it correct ?

If I multiply through by 1294 I get

X = (1294 *14851/15604) + (1294 * X / 15604)

and I don't see how the right hand side can simplify into the above expression.

so can you teach me how this works (I reckon this has been troubling me for at least 40 years)
• May 6th 2011, 04:58 AM
Ackbeet
Quote:

Originally Posted by NigelS
Hi,

X/1294 = (14851 + X) / 15604

=>

X = 1294 * 14851/ (15604 - 1294)

I can't see how this is done, is it correct ?

If I multiply through by 1294 I get

X = (1294 *14851/15604) + (1294 * X / 15604)

and I don't see how the right hand side can simplify into the above expression.

It doesn't. What you have to do is get all the terms with X in them over to one side of the equation. So the 1294 * X / 15604 term on the RHS needs to join the other plain X term on the LHS. How could you do that?
• May 6th 2011, 04:59 AM
earboth
Quote:

Originally Posted by NigelS
Hi,

X/1294 = (14851 + X) / 15604

=>

X = 1294 * 14851/ (15604 - 1294)

I can't see how this is done, is it correct ?

If I multiply through by 1294 I get

X = (1294 *14851/15604) + (1294 * X / 15604)

and I don't see how the right hand side can simplify into the above expression.

so can you teach me how this works (I reckon this has been troubling me for at least 40 years)

1. Multiply both sides by 15604.

2. Subtract on both sides 1294*x

3. Factor out x at the LHS.

4. Divide both sides by the term in parantheses.
• May 6th 2011, 08:59 AM
NigelS
Quote:

Originally Posted by Ackbeet
It doesn't. What you have to do is get all the terms with X in them over to one side of the equation. So the 1294 * X / 15604 term on the RHS needs to join the other plain X term on the LHS. How could you do that?

I replied in detail with my working but the post was lost

Basically

X/1294 = (14851 + X) / 15604

X/a = (b+x)/ c

X = ab/c + ax/c

X - ax/c = ab/c

X*(1- a/c) = ab/c

1- (a/c) = (c-a)/c

X= (ab/c) / (c-a)/c
or even
x = ab/c *c/c-a

X = ab/c-a

Ok so I've managed it - is this a generic transformation, is there a rule, or do I have to do the algebra each time ....

X = 1294 * 14851/ (15604 - 1294)

X = ab/c - a
• May 6th 2011, 09:37 AM
Ackbeet
Your general formula appears to be correct. I would not memorize it. Know the rules of algebra and apply them each time. Once you're very comfortable with the rules of algebra, and only then, I would probably use a CAS to solve it.
• May 6th 2011, 10:25 AM
bjhopper
Simplifing equation
Hi Nigels,
Solve this x/12 =15 +x/16check the answer