Problem 125 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When checking a radical equation's proposed solution, I can substitute into the original equation or any equation that is part of the solution process.

Step-by-Step Solution

Answer

The statement partially does not make sense, as proposed solutions should always be verified in the original equation to exclude the possibility of extraneous solutions which may have appeared during the solution process.

Step 1: Consider the Statement

The given statement is as follows: 'When checking a radical equation's proposed solution, I can substitute into the original equation or any equation that is part of the solution process.'

Step 2: Analyze the Statement

Radical equations often involve square roots, cube roots, and other types of roots. A correct solution to a radical equation should satisfy the original equation. Moreover, it should not necessarily satisfy the transformed versions of the original equation due to the occurrence of extraneous solutions. Extraneous solutions are solutions that are valid for the transformed equation but not for the original equation.

Step 3: Evaluate the Statement

Based on the reasoning in the previous step, the given statement does not make complete sense. Substitute the solution only into the original equation to verify the proposed solution. Checking the proposed solutions in only transformed equations can lead to the inclusion of extraneous solutions which do not satisfy the original equation.