checking a solution

Checking a solution is the math version of re-reading a text before you hit send. You take the value you found, put it back into the original equation, and see whether the two sides really agree. If they do, your answer holds up; if not, an error slipped in somewhere.

Substitute the value for the variable everywhere it appears in the original equation — not a rearranged version, which may already carry your mistake. Then simplify each side independently. A genuine solution makes the left side equal the right side, plain and simple.

This step is more than tidiness. Certain operations, like squaring both sides or clearing denominators, can introduce extraneous solutions that satisfy a transformed equation but fail the original. Checking is the only reliable way to catch and discard them.