Final answer:
It is impossible to confirm which statement about x is true without the original equation. An extraneous solution arises when it satisfies the squared form of the equation but not the original. You must check all solutions against the original equation to determine their validity. Option 3,4 are correct.
Step-by-step explanation:
Without the original equation or context in which values of x are being considered, it is impossible to determine definitively which statement about x is true. However, based on the information provided, the concept of an extraneous solution typically arises when solving equations that involve a squared term or radical expressions, where a solution may satisfy the squared form of the equation but not the original equation.
In an example involving quadratic equations, after using the quadratic formula to find the two possible values of x, one might be extraneous if it does not satisfy the original equation. It is important to always check both possible solutions by substituting them back into the original equation to see which (if any) are extraneous.
Option 1 might suggest that after solving the equation, the solution x = –4 does not satisfy the original equation, making it an extraneous solution. Option 2 would mean that x = –4 does, indeed, satisfy the original equation and thus is a true solution. A similar rationale would apply to Options 3 and 4 for the value x = 4.