We are given the equation $\frac{2f(x)-5}{x+3}=4$ and asked to find $f(x)$ as $x$ approaches 2.

1. Problem Description

We are given the equation $\frac{2f(x)-5}{x+3}=4$ and asked to find $f(x)$ as $x$ approaches

2.

2. Solution Steps

First, we solve for $f(x)$ in terms of $x$.

Multiply both sides of the equation by $x+3$:

$2f(x) - 5 = 4(x+3)$

$2f(x) - 5 = 4x + 12$

Add 5 to both sides:

$2f(x) = 4x + 12 + 5$

$2f(x) = 4x + 17$

Divide both sides by 2:

$f(x) = \frac{4x + 17}{2}$

Now we can evaluate the limit as $x$ approaches 2:

$\lim_{x \to 2} f(x) = \lim_{x \to 2} \frac{4x+17}{2}$

Since the function is continuous at $x=2$, we can substitute $x=2$:

$f(2) = \frac{4(2) + 17}{2}$

$f(2) = \frac{8 + 17}{2}$

$f(2) = \frac{25}{2}$

3. Final Answer

$\frac{25}{2}$