Answer :
To determine which value of [tex]\(x\)[/tex] makes the rational expression [tex]\(\frac{16-x}{7+x}\)[/tex] undefined, we need to focus on the denominator. A rational expression becomes undefined when its denominator is equal to zero, so we need to find the value of [tex]\(x\)[/tex] that makes [tex]\(7 + x = 0\)[/tex].
Here’s how we can solve this step-by-step:
1. Set the denominator equal to zero:
[tex]\[
7 + x = 0
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], subtract 7 from both sides:
[tex]\[
x = -7
\][/tex]
The value of [tex]\(x\)[/tex] that makes the denominator zero is [tex]\(x = -7\)[/tex]. Therefore, the rational expression [tex]\(\frac{16-x}{7+x}\)[/tex] is undefined when [tex]\(x = -7\)[/tex].
Thus, the correct answer is C. -7.
Here’s how we can solve this step-by-step:
1. Set the denominator equal to zero:
[tex]\[
7 + x = 0
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], subtract 7 from both sides:
[tex]\[
x = -7
\][/tex]
The value of [tex]\(x\)[/tex] that makes the denominator zero is [tex]\(x = -7\)[/tex]. Therefore, the rational expression [tex]\(\frac{16-x}{7+x}\)[/tex] is undefined when [tex]\(x = -7\)[/tex].
Thus, the correct answer is C. -7.
