Answer :
To determine which value of [tex]\( x \)[/tex] makes the rational expression [tex]\(\frac{16-x}{7+x}\)[/tex] undefined, we need to find out when the denominator equals zero. A rational expression is undefined whenever its denominator is zero because division by zero is not allowed in mathematics.
Let's break it down step-by-step:
1. Identify the Denominator:
For the expression [tex]\(\frac{16-x}{7+x}\)[/tex], the denominator is [tex]\(7 + x\)[/tex].
2. Set the Denominator to Zero:
We want to find the value of [tex]\( x \)[/tex] that makes [tex]\(7 + x = 0\)[/tex].
3. Solve the Equation:
[tex]\[
7 + x = 0
\][/tex]
Subtract 7 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = -7
\][/tex]
4. Conclusion:
The value [tex]\( x = -7 \)[/tex] makes the denominator zero, and therefore, makes the expression undefined.
Therefore, the correct answer is A. -7.
Let's break it down step-by-step:
1. Identify the Denominator:
For the expression [tex]\(\frac{16-x}{7+x}\)[/tex], the denominator is [tex]\(7 + x\)[/tex].
2. Set the Denominator to Zero:
We want to find the value of [tex]\( x \)[/tex] that makes [tex]\(7 + x = 0\)[/tex].
3. Solve the Equation:
[tex]\[
7 + x = 0
\][/tex]
Subtract 7 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = -7
\][/tex]
4. Conclusion:
The value [tex]\( x = -7 \)[/tex] makes the denominator zero, and therefore, makes the expression undefined.
Therefore, the correct answer is A. -7.
