Question

A student solves the following equation for all possible values of x: 8 Over x + 2 =2 Over x minus 4

His solution is as follows:
Step 1: 8(x – 4) = 2(x + 2)
Step 2: 4(x – 4) = (x + 2)
Step 3: 4x – 16 = x + 2
Step 4: 3x = 18
Step 5: x = 6
He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.
Which best describes the reasonableness of the student’s solution?
His solution for x is correct and his explanation of the extraneous solution is reasonable.
His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.
His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.
His solution for x is incorrect. When solved correctly, there are no extraneous solutions.

Answer 1

Explanation:

The student's solution for x is correct. They correctly solved the given equation step by step and determined that x = 6.

However, their explanation for why 6 is an extraneous solution is not accurate. In order for a solution to be extraneous, it must result in a denominator being equal to zero when substituted back into the original equation. In this case, the student's explanation that the 6s cancel to 0 is incorrect.

Therefore, the correct assessment of the reasonableness of the student's solution is that their solution for x is correct, but their explanation for why 6 is an extraneous solution is not accurate.