To determine where the rational expression [tex]\(\frac{2x + 4}{x - 7}\)[/tex] is undefined, we need to look at the denominator. A rational expression is undefined wherever the denominator is equal to zero because division by zero is not defined in mathematics.
The denominator of the given expression is [tex]\(x - 7\)[/tex]. We need to find the value of [tex]\(x\)[/tex] that makes this denominator equal to zero.
Let's set the denominator equal to zero and solve for [tex]\(x\)[/tex]:
[tex]\[
x - 7 = 0
\][/tex]
Add 7 to both sides of the equation to isolate [tex]\(x\)[/tex]:
[tex]\[
x = 7
\][/tex]
Therefore, the rational expression [tex]\(\frac{2x + 4}{x - 7}\)[/tex] is undefined when [tex]\(x\)[/tex] is equal to 7.
Thus, the value of [tex]\(x\)[/tex] that makes the expression undefined is:
[tex]\[
\boxed{7}
\][/tex]
