Solve [tex]\frac{4}{x}+1=y+13[/tex] for [tex]x[/tex].

A. [tex]x=\frac{4}{y+12}[/tex]
B. [tex]x=\frac{12}{y}[/tex]
C. [tex]x=\frac{y+12}{4}[/tex]
D. [tex]x=\frac{y+12}{14}[/tex]



Answer :

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].

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