Do you agree? Explain why or why not.

Answer:

I do not agree with the student. While solving the equation results in x 4, this is an extraneous solution. When you substitute 4 back into the original equation, you get sqrt(2(4) 1) 3 0, which simplifies to 3 3 0, or 6 0. Since this is a false statement, x 4 is not a solution. Furthermore, the equation sqrt(2x 1) 3 has no real solution because a principal square root cannot be negative.