When solving equations, what is a good practice to avoid extraneous solutions?

When solving equations, what is a good practice to avoid extraneous solutions?

• A. Check your potential solutions in the original equation
• B. Ignore negative solutions
• C. Only verify the final result
• D. Assume all derived solutions are valid

Answer: (A)

When solving equations, a good practice is to verify any potential solutions by substituting them back into the original equation. This helps catch extraneous solutions that can appear from certain algebraic steps, like squaring both sides or multiplying by expressions that could be zero, which can change the equation’s truth set even though the manipulated form seems to be satisfied. For example, if you solve a radical equation by squaring both sides, you might end up with candidates that satisfy the squared version but not the original. Substituting back shows which ones truly work, and it ensures you haven’t accepted something that only fits the manipulated form. So checking every potential solution in the original equation is the most reliable way to avoid including false results.

When solving equations, a good practice is to verify any potential solutions by substituting them back into the original equation. This helps catch extraneous solutions that can appear from certain algebraic steps, like squaring both sides or multiplying by expressions that could be zero, which can change the equation’s truth set even though the manipulated form seems to be satisfied.

For example, if you solve a radical equation by squaring both sides, you might end up with candidates that satisfy the squared version but not the original. Substituting back shows which ones truly work, and it ensures you haven’t accepted something that only fits the manipulated form.

So checking every potential solution in the original equation is the most reliable way to avoid including false results.