Final answer:
To evaluate (mn)(x) for x = -3, substitute -3 for x in the expression (mn)(x). The result is 9mn(-3), which is undefined.
Step-by-step explanation:
To evaluate (mn)(x) for x = -3, we simply substitute -3 for x in the expression. So (mn)(-3) = 9m n(-3). Since (-3) is different from 0, the correct answer is D) Undefined. It is important to note that when evaluating an expression for a specific value of x, we replace every instance of x in the expression with the given value.
In this case, we are replacing x with -3.Also, the expression seems to suggest a restriction or a point where the equation is not valid and asks for x ≠ ______ (?). Since the equation (mn)(-3) = 9m * n(x) suggests that the value of x specifically cannot be -3 when the equation holds, because we are given (mn)(-3) as a defined value equal to 9m * n(x), the blank in the question likely refers to the value we pick for x on the right-hand side of the equation to ensure it does not conflict with the left-hand side, which has x already as -3.
As for the choices provided: A) -3 - It is clear that when x = -3, (mn)(-3) is already given, so this value would not make sense, because it would imply (mn)(-3) equal to itself times a constant which is not logical. B) 0 - There’s no mention that x cannot be 0 or that it would create any issues in the expression, so there’s no reason to choose this option for the excluded value for x. C) 3 - Likewise, nothing in the information provided suggests any problems with x = 3. D) Undefined - It does not directly answer what x cannot be without additional context.
The correct exclusion would actually be choice A), -3, but it is worth noting that the expression and the question are quite ambiguous and incomplete.
Traditional algebra dictates that we should avoid a value for which the equation becomes undefined or contradictory. Therefore, since we are given (mn)(-3), we naturally exclude -3 from the right-hand side of the equation (x in 9m * n(x)) to avoid the conflict of taking the product of m and n at x = -3 and then trying to equate it to itself multiplied by a constant (9m).