"We excluded the value of 𝑥=−13x=− 31​  because __________."there can only be one answer to an equationit results in the argument being negative

To complete the statement "We excluded the value of $x = -31$ because __________," you should consider the context in which $x = -31$ was excluded. Given the options provided:

1. There can only be one answer to an equation: This option suggests that the equation solved either does not permit multiple solutions or that $x = -31$ results in a condition where it violates a mathematical principle.
2. It results in the argument being negative: This would be relevant if $x = -31$ leads to a negative value under a square root or logarithm, thus making the expression undefined in real numbers.

Given these choices, the most likely and relevant reason for the exclusion of $x = -31$ would be that "it results in the argument being negative." Therefore, the completed statement would be:

"We excluded the value of $x = -31$ because it results in the argument being negative."

This indicates that including $x = -31$ would lead to an undefined or non-real result in the context of the function being analyzed.