To solve the equation [tex]\(\frac{4}{x} + 1 = y + 13\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Isolate [tex]\(\frac{4}{x}\)[/tex]:
[tex]\[
\frac{4}{x} = y + 13 - 1
\][/tex]
Simplifying the right-hand side:
[tex]\[
\frac{4}{x} = y + 12
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Multiply both sides of the equation by [tex]\(x\)[/tex] to get rid of the fraction:
[tex]\[
4 = x \cdot (y + 12)
\][/tex]
3. Next, isolate [tex]\(x\)[/tex] by dividing both sides by [tex]\(y + 12\)[/tex]:
[tex]\[
x = \frac{4}{y + 12}
\][/tex]
Comparing this result with the given multiple-choice answers:
[tex]\[
\begin{align*}
\text{Choice 1:} &\quad x = \frac{4}{y + 12} \\
\text{Choice 2:} &\quad x = \frac{12}{y} \\
\text{Choice 3:} &\quad x = \frac{y + 12}{4} \\
\text{Choice 4:} &\quad x = \frac{y + 12}{14}
\end{align*}
\][/tex]
The correct answer is:
[tex]\[
x = \frac{4}{y + 12}
\][/tex]
So the correct option is the first one:
Option 1: [tex]\(x = \frac{4}{y + 12}\)[/tex].
