We are given:
[tex] 14 =\frac{4y-6x}{3}[/tex]
Since we are solving for y, we need to isolate y on one side of the equation. The first step is removing the denominator by multiplying both sides by 3.
[tex] 3(14)=3(\frac{4y-6x}{3}) [/tex]
When we do that, the denominator cancels out and we are left with:
[tex] 42=4y-6x [/tex]
To solve for y, we need to isolate y on one side of the equation without a coefficient next to it. Add 6x to both sides, which leaves 4y on one side of the equation.
[tex] 6x+42=4y [/tex]
Divide both sides by 4 to remove the coefficient on the 4y.
[tex] \frac{6x+42}{4}=\frac{4y}{4} [/tex]
Your simplified answer would be:
[tex] y=\frac{6x+42}{4} [/tex]
HOWEVER, you are not done. The fraction can be simplified into simpler terms.
All of the terms in the fraction are divisible by 2. You need to divide all of the terms by 2. When you do that, you get:
[tex] y=\frac{3x+21}{2} [/tex]
This equation above is the simplest y can get and, therefore, is your final answer.
