Thread: Sipplifying equations with x on both sides and additions

Hi,
I read this

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)

Originally Posted by NigelS

Hi,
I read this

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?

Originally Posted by NigelS

Hi,
I read this

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.

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?

Adrian Thanks.

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

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.

Hi Nigels,
Solve this x/12 =15 +x/16check the answer
Solve your problem in the same manner.check the answer.
I solve this by cross multiplying 16x =12(15+x)


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