To determine which value is equivalent to [tex]\(\frac{x-7}{7-x}\)[/tex], let's analyze and simplify the expression step-by-step.
Consider the given expression:
[tex]\[
\frac{x-7}{7-x}
\][/tex]
Notice that we can rewrite the denominator [tex]\(7 - x\)[/tex] by factoring out a [tex]\(-1\)[/tex]:
[tex]\[
7 - x = -(x - 7)
\][/tex]
So the original expression becomes:
[tex]\[
\frac{x-7}{7-x} = \frac{x-7}{-(x-7)} = \frac{x-7}{-1 \cdot (x-7)}
\][/tex]
The [tex]\((x-7)\)[/tex] terms in the numerator and the denominator cancel each other out, leaving:
[tex]\[
\frac{x-7}{-(x-7)} = -1
\][/tex]
Thus, the simplified value of [tex]\(\frac{x-7}{7-x}\)[/tex] is:
[tex]\[
-1
\][/tex]
The correct value equivalent to [tex]\(\frac{x-7}{7-x}\)[/tex] is [tex]\(\boxed{-1}\)[/tex].
