Check a Proposed Solution

Check a proposed solution

When you are asked to check a proposed solution, your job is to decide whether the given answer really works for the original algebra problem.

1) Start with the original statement

Read the equation or expression carefully. A proposed solution may look reasonable, but it must satisfy the original problem exactly.

2) Substitute or test the answer

Replace the variable with the proposed value. Then simplify step by step. If the result makes a true statement, the solution works. If it produces a false statement, the solution is not valid.

3) Watch for simplification errors

Carry out arithmetic carefully, especially with signs, fractions, and distribution. A wrong check often comes from a small algebra mistake rather than the idea itself.

4) Compare both sides

If you are checking an equation, simplify both sides after substitution. The solution is correct only if both sides match or the equation becomes true.

5) Write the conclusion clearly

State whether the proposed solution is valid or not, and give the simplified final result if needed.

Quick check

If the answer is supposed to be a solution, plugging it back in should make the original statement true. If not, it is rejected.