Problem 125 - Algebra and Trigonometry

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 does make sense, but with caution. It's always the best practice to substitute the proposed solution back into the original radical equation as it eliminates any chance of errors that might have occurred while manipulating the equation during the solution process.

Step 1: Understanding The Statement

Looking at the statement, it is said that while checking a radical equation, the proposed solution can be substituted into the original equation or any equation that is part of the solution process.

Step 2: Analyzing The Statement

The process of solving equations sometimes involves manipulating the original equation into several forms. These manipulations are equivalent to the original equation, thus these new forms have the same solution as the original equation and should also confirm the proposed solution.

Step 3: Final Verification Step

However, it is always the safest practice to substitute the proposed solution into the original equation because even a tiny manipulation error during the process of solving could lead to a different equation, and thus, an incorrect solution if you only checked your solution using it.