11- \frac{1}{2} y=3+6x
Taking y to the other side;
11-3-6x= \frac{1}{2} y
8-6x= \frac{1}{2}y
Multiply each side by 2
16-12x=y
y=16-12x
So, since we have [tex] 11-\frac{2}{y}=3+6x [/tex], and we want to solve for y, that means we should first get y out of the denominator so we can manipulate it better, so multiplying the whole equation by y yields:
[tex] 11y-2=y(3+6x) [/tex]
So, now we want to bring all the ys to one side and the rest of the variables and constants to the other, that gives us:
[tex] 11y-y(3+6x)=2 [/tex]
Factoring y out of the RHS gives us:
[tex] y(11-(3+6x))=2\implies \\
y(11-3-6x)=2 \implies \\
y(-6x+8)=2 [/tex]
So, now we want to divide both sides by (-6x+8) to get y by itself:
[tex] y=\frac{2}{-6x+8} \implies
y=\frac{1}{-3x+4} [/tex]
With that we have solved for y.
