Answer :
To determine when the rational expression [tex]\(\frac{16x}{7-x}\)[/tex] is undefined, we need to focus on the denominator, [tex]\(7-x\)[/tex]. A rational expression becomes undefined when its denominator is equal to zero because division by zero is not allowed in mathematics.
1. Start with the denominator: [tex]\(7 - x\)[/tex]
2. Set the denominator equal to zero to find the value of [tex]\(x\)[/tex] that makes it zero:
[tex]\[
7 - x = 0
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
-x = -7
\][/tex]
Multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[
x = 7
\][/tex]
Therefore, the rational expression [tex]\(\frac{16x}{7-x}\)[/tex] is undefined when [tex]\(x = 7\)[/tex].
So, the correct choice is:
A. 7
1. Start with the denominator: [tex]\(7 - x\)[/tex]
2. Set the denominator equal to zero to find the value of [tex]\(x\)[/tex] that makes it zero:
[tex]\[
7 - x = 0
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
-x = -7
\][/tex]
Multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[
x = 7
\][/tex]
Therefore, the rational expression [tex]\(\frac{16x}{7-x}\)[/tex] is undefined when [tex]\(x = 7\)[/tex].
So, the correct choice is:
A. 7
