Constant

Notation

In

$$3x + 7 = 22$$

both $7$ and $22$ are constants. The $3$ is not — it is attached to $x$, which makes it a coefficient.

Why the distinction matters when solving

Constants and variable terms move differently. You undo a constant by adding or subtracting it, and you undo a coefficient by dividing. Treating $3x + 7$ as though the $3$ and the $7$ were the same kind of thing is the error behind subtracting $3$ from both sides, which accomplishes nothing.

Constants that are letters

In $y = mx + b$, the letters $m$ and $b$ are constants for a particular line, even though they are letters. They hold still while $x$ and $y$ vary. This is the idea you use throughout literal equations: a symbol counts as constant when it is not the thing you are solving for.