1 Equation: rearrange y = (2x + 1) / (x - 3) in terms of x

[jaydstein]

The equation that I am given is:
y = (2x+1)/(x-3)

I need to rearrange the equation in terms of x. I'm stumped. Any suggestions?

 

[masters]

Multiply both sides of the equation by (x-3). Distribute the y and isolate the x terms.

 

[jaydstein]

May as well bring this up this question while I'm here:

solution 1:
y = (2x+1)/(x-3)
y - (7/(x-3)) = (2x+1)/(x-3) - (7/(x-3)) = (2(x-3))/(x-3) = 2
y = 2 + (7/(x-3))
(y-2)/7 = (x-3)^-1
7/(y-2) = x-3
7/((y-2) + 3 = x
ie x = 7/(y-2) + 3

solution 2:
y = (2x+1)/(x-3)
y(x-3) = 2x+1
yx-3y = 2x+1
yx -2x = 3y+1
x(y-2) = 3y+1
x = (3y+1)/(y-2)

Are the two different solutions equivalent, or am I screwing up again? :mrgreen:

 

[masters]

I believe I'd go with solution #2.