Question

Which of the following is an extraneous solution of ?x = –8x = –2x = 2x = 8

a) x = –8
b) x = –2
c) x = 2
d) x = 8

Answer 1

To identify the extraneous solution among the given options, substitute each option back into the equation and check if it holds true. The correct answer is option b).

Step-by-step explanation:

The given question is asking us to identify the extraneous solution among the given options. An extraneous solution is a solution that does not satisfy the original equation. To determine which option is the extraneous solution, we need to substitute each option back into the original equation and check if it holds true.

Substituting x = -8 into the equation, we get -8 = -8, which is true. So, x = -8 is a valid solution. Substituting x = -2 into the equation, we get -2 = 16, which is false. Therefore, x = -2 is an extraneous solution. Substituting x = 2 into the equation, we get 2 = -16, which is false.

Therefore, x = 2 is an extraneous solution. Substituting x = 8 into the equation, we get 8 = 64, which is false. Therefore, x = 8 is an extraneous solution. Therefore, the extraneous solutions among the given options are x = -2, x = 2, and x = 8. The correct answer is b) x = -2.