What Solving Means

n + 4 = 9 is a claim. It is true for some values of n and false for others.

The value that makes it true has a name.

Solution is a value that makes an equation true when substituted.

Testing is allowed

Trying n = 6 gives 10, which is too big. Trying n = 5 gives 9, which is true.

The equals sign is a balance

It does not mean "the answer is". It says both sides are the same amount.

A solution makes the sentence true

The equation n + 3 = 8 is a claim that becomes true for some values of n and false for others. Solving means finding every value that makes it true — here, just 5. An equation is a question about which numbers work.

Checking a proposed solution

Substitute your answer back into the original equation: 5 + 3 = 8 is true, so 5 is a solution. This check is not optional politeness — it is what distinguishes a solution from a guess, and it catches most arithmetic slips.

Equations and expressions are different

3n + 5 is an expression: it has a value once you know n. And 3n + 5 = 20 is an equation: it is true or false depending on n. You evaluate an expression and you solve an equation. Confusing the two makes both harder.

How many solutions there can be

Most equations here have exactly one solution. Some have none: n + 1 = n is never true. Some have infinitely many: n + 1 = 1 + n is always true. Noticing which kind you have is part of solving, not a separate topic.