Certainly! Let's solve the given equation step-by-step.
The equation provided is:
[tex]\[ \frac{4}{x} + 1 = y + 13 \][/tex]
Our task is to solve for [tex]\( x \)[/tex]. Here are the steps:
1. Isolate the fractional term: To isolate [tex]\( \frac{4}{x} \)[/tex], first subtract 1 from both sides of the equation.
[tex]\[ \frac{4}{x} + 1 - 1 = y + 13 - 1 \][/tex]
Simplifying the equation, we get:
[tex]\[ \frac{4}{x} = y + 12 \][/tex]
2. Solve for [tex]\( x \)[/tex]: To eliminate the fraction, consider inverting both sides of the equation. We need to express [tex]\( x \)[/tex] explicitly.
[tex]\[ x = \frac{4}{y + 12} \][/tex]
Thus, the solution we arrived at is:
[tex]\[ x = \frac{4}{y + 12} \][/tex]
So, the correct answer among the given options is:
[tex]\[ x = \frac{4}{y + 12} \][/tex]
Therefore, the correct option corresponds to [tex]\( \boxed{1} \)[/tex].
