Solve  \[\frac{x+4}{x-2}=3\]for $x$.
To solve for $x$, I need to isolate it on one side of the equation. First, I can multiply both sides by $x-2$ to clear the fraction. This gives me \[x+4=3x-6\]. Next, I can subtract $x$ from both sides to get \[4=2x-6\]. Then, I can add $6$ to both sides to get \[10=2x\]. Finally, I can divide both sides by $2$ to get \[x=5\]. To check my answer, I can plug it back into the original equation and see if it makes it true. I get \[\frac{5+4}{5-2}=3\], which simplifies to \[\frac{9}{3}=3\], which is true. So $x=5$ is the correct solution. 