Question 266·Medium·Advanced Math

You need $m$ alone. Since $2n$ is added to the term containing $m$, subtract $2n$ from both sides:

The $3$ multiplies $\sqrt m$, so divide both sides by $3$: $\sqrt m=\frac{p-2n}{3}$. This gives $\sqrt m$, not $m$. There’s one operation left to undo.

For a numerical checkpoint, choose $n=2$ and $p=13$. These allow positive $m$ because $13>2(2)$. Type $n=2$, $p=13$, and $3\sqrt{m_1}+2n\sim p\{m_1>0\}$; the tilde tells Desmos to find $m_1$. It reports $m_1=9$ under PARAMETERS. Type $\frac{p-2n}{3}$, and Desmos prints $3$. That’s $\sqrt m$, not $m$. One example checks the distinction; it doesn’t prove a formula.

Now that the root is alone, square both whole sides to undo it:

Simplify the left side: $m=\left(\frac{p-2n}{3}\right)^2$. Square the entire fraction, not only its denominator. This expresses $m$ in terms of $n$ and $p$. Choice B.