Question

Make 'X' the subject troubles

Answer 1

Not sure if this is exactly what you mean, but generally if there's any fractions involved, we can multiply through (multiply both sides) by a common multiple of the denominators. Ie. (3x+1)/4=(2x-5)/6 => 3(3x+1)=2(2x-5), where we've multiplied both sides of the equation by 12 (the lowest common multiple of 4 and 6). From this point here 3(3x+1)=2(2x-5), would you feel comfortable knowing how to solve?

Answer 2

>How do I make X the subject, if 'X' appears on both sides of the '='

You have to find a way to get all the x's on the same side. Some forms are easier than others.

>... for example 2X = 6X over 5Z + 8Z

That is (using lower case)

2x = 6x/(5z + 8z)

Well first of all those terms in the bottom can be combined.

2x = 6x/13z

Generally when you have a fraction, you're going to want to multiply by the denominator so it's not a fraction any more. So multiply both sides by 13z.

26xz = 6x

Now, finally, you can move all the x terms to the same side. Let's subtract the 6x from both sides so you no longer have an x on the right.

26xz - 6x = 0

And you can factor out an x

x(26z - 6) = 0

And you can divide both sides by the thing in parentheses

x(26z - 6)/(26z - 6) = 0/(26z - 6)

x = 0

To summarize, when you have fractions involved, it's often this process

* Clear fractions by multiplying by the denominator
* Move all the x terms to the same side
* Factor out the x
* Divide by the thing multiplying x

Feel free to ask with more complicated examples.