The operation $\nabla$ is defined by $a \nabla b=(a+1)(b-2)$ for real numbers $a$ and $b$. For example, $4 \nabla 5=(4+1)(5-2)=15$. If $5 \nabla x=30$, what is the value of $x$ ?
Using the definition of $\nabla$,

$$
\begin{aligned}
5 \nabla x & =30 \\
(5+1)(x-2) & =30 \\
6(x-2) & =30 \\
x-2 & =5
\end{aligned}
$$

and so $x=7$.

ANSWER: $x=7$