How the heck do you isolate x?

Question

AHHHHHHHH!!! After asking several people I haven't been able to figure out this simple algebra for my calculus class... so how do I isolate x?

[(4x-3)/(2x+1)]=y

Answer 1

(4x - 3) / (2x + 1) = y

First thing you need to do is multiply both sides by (2x + 1).

4x - 3 = y(2x + 1)

Now, distribute the y over the brackets.

4x - 3 = 2xy + y

Move *everything* with an x in it to the left hand side; everything else goes to the right hand side.

4x - 2xy = y + 3

Factor an x out.

x(4 - 2y) = y + 3

Now, divide both sides by (4 - 2y)

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

Answer 2

In some sense it IS isolated since it is only on the left. One can also do:

4x-3=(2x+1)y
collect all x on left
x(4-2y)-3=y
x(4-2y)=(y+3)
x=(y+3)/(4-2y)

Answer 3

multiply each side by (2x+1)
this gives 4x-3 = 2xy + y add 3 to each side
this gives 4x = 2xy +y +3 divide each side by 4
this gives you x = (2xy +y+3)/4


probably

Answer 4

(4x-3)=y(2x+1)
4x-3-2yx-y=0
2x(2-y)-3-y=0
2x(2-y)=y+3
2x=(y+3)/(2-y)
x=(y+3)/2(2-y)