To determine which value of [tex]\( x \)[/tex] makes the rational expression [tex]\(\frac{16-x}{7+x}\)[/tex] undefined, we need to identify when the denominator is zero. A rational expression becomes undefined when its denominator equals zero, as division by zero is undefined.
Let’s examine the denominator [tex]\( 7 + x \)[/tex]:
1. Set the denominator equal to zero:
[tex]\[
7 + x = 0
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = -7
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the denominator zero, and thus the rational expression undefined, is [tex]\( -7 \)[/tex].
So, the correct answer is:
B. [tex]\(-7\)[/tex]
