how do you rearrange this equation?

Question

say you had an equation like this: 3x - 2 = 4x + 3y / 2xy
[the 2xy is underneath the 3y]
If you wanted to multiply by 2xy in order to get rid of it would you also multiply the 4x on the right hand side by 2xy or just all of the terms on the left?

Answer 1

First isolate the 3y/2xy so it is easier to see:
start with:
3x-2=4x+ 3y/2xy
subtract 4x from both sides:
-x-2=3y/2xy
now multiply by 2xy:
2xy(-x-2)=3y
or:
-2x^2-4xy=3y
let's multiply both sides by -1 to clean things up
2x^2+4xy=-3y
move the -3y to the other side (add 3y to both sides)
2x^2+4xy+3y=0
how far did you need to go?

To answer the second question:
The process is to multiply both sides by 2xy, that means that the 4x would be multiplied by 2xy as well. I just avoided it by subtracting the 4x out of the right side before I multiplied. It still happens, but now the 4x is on the other side (as -4x, which combined with the 3x and reduced to -x)

Answer 2

you need to multiply both side so that equation remains unchanged

(3x-2) 2xy=(4x+3y/2xy)2xy
it will convert to
6y(X^2)-4xy =8y(x^2)+3y

but if i am correct you dont wish to do this you wish to simplify your equation

which is 3x-2=4x+(3y/2xy)

you may cancel both y in numerator and denominator of the bracket


so that you have 3/2x

now again just to make tings clear to you
we can write question as
3x-2=(4x/1)+(3/2x)

we can multiply lhs with the denominator of rhs but only if each has common
which can be done by writing 4x/1
as (4x/1)*(x/x)since multiplying both numeratorr and denomiantor by 1 does not change it .
so we can take x to lhs and we have
(3x-2)x=4x^2+3/2

Answer 3

Try it for yourself to see who's right:

3x-2 = 4x + 3y/2xy

If you multiply all the LHS by 2xy you have to do the same to the RHS. So

2xy(3x-2) = 2xy(4x + 3y/2xy)

Now expand...
6x^2y - 4xy = 8x^2y + 3y.

By the way, 3y/2xy simplifies to 3/2x so you could have done this with 2x instead.

Answer 4

First simplify your equation. You can't multiply the 4x times 2xy. you would have to multiply that on the opposite side of the equal sign.

Answer 5

each term must be multiplied by 2xy in order to preserve the equality. Remember "What you do to one side(term) you must do to the other"

ie; next line would be:

6(x^2)y - 12xy = 8(x^2)y + 3y

Answer 6

Firstly, y can be cancelled out, as it occurs top and bottom in the last term.

Then, multiply through (all terms, both sides) by x.

Collect up the terms into the standard form of a quadratic:
ax^2+bx+c=0

Answer 7

3y/(2xy)= 3/(2x)

so you have 3x-2=4x+3/(2x)
so 6x^2 - 4x = 8x^2 + 3
so 2x^2 + 4x + 3 = 0
ie there are two solutions of x to the quadratic equation and y can be anything you like.

Answer 8

You have to multiply everything--the fraction, the 4x, AND all the stuff on the other side.

Answer 9

just the 2xy

Answer 10

All terms on LHS - explanation to follow