What is an extraneous solution?

• A. An extraneous solution is a false answer that can be derived when attempting to solve for an equation; ALWAYS check your answers.
• B. A solution that satisfies the original equation after all steps.
• C. A method used to solve linear equations.
• D. A value that makes both sides equal in an equation.

Answer: (A)

Extraneous solutions come from the algebraic steps you use to solve an equation that can introduce extra possibilities not allowed by the original problem. They appear when the manipulation creates a equation that has solutions that don’t actually satisfy the original equation, such as squaring both sides, clearing denominators, or multiplying by something that could be zero. The key idea is to treat them as candidates that must be checked in the original equation.

That’s why the correct description is that an extraneous solution is a false answer that can be derived during solving and should be verified by substitution back into the original equation. Always check all potential solutions in the original setup to confirm which ones truly work.

For clarity, consider a situation where squaring both sides yields extra roots that don’t fit the original relationship; those extra roots are extraneous.