What does it mean to solve an expression in terms of a variable?

Question

If i have this:

$a + p = 3$, what means express in terms of $a$? , I know that this is elementary, and although I know how to do more difficult things, I have overlooked it.

Answer 1

$a + p = 3 \iff a= 3 - p \iff p=3-a$.

To express something "in terms of" variables, is to have an expression with variables in which the variables, although unknown, are considered constants.

"$a+p$" is an expression "in terms of $a$ and $p$". If we knew what $a$ and $p$ were that expression would simply be a single value

"$3-p$" is an expression "in terms of $p$". And "$3-a$" is an expression "in terms of $a$" for the same reasons.

To solve something is to state: "I know what IT is: IT = $blahblahblah$"

$a + p = 3$ is a "solution" for $a + p$. We know exactly what $a + p$ is (unfortunately we don't know what either $a$ are $p$ individually are.)

$p = 3-a$ is a "solution" for $p$. We know that $p$ is definitely $3-a$. Now, you might point out that we don't actually know what $p$ is precisely because we don't actually know what $a$ is. And that's true.

This is a solution "in terms of $a$". We don't know what $p$ objectively is, but we do know what it is "in terms of $a$". Whatever $a$ is.... $p$ is going to be $3$ minus that.

Likewise $a = 3-p$ is a solution for $a$ in terms of $p$.