Answer
$\lim\limits_{x \to 4} (2x-5)= 3$
Work Step by Step
Let $\epsilon \gt 0$ be given.
Let $\delta = \frac{\epsilon}{2}$
Suppose that $\vert x-4 \vert \lt \delta$.
Then:
$\vert (2x-5)-3 \vert = \vert 2x-8 \vert = \vert 2(x-4) \vert = 2\vert x-4 \vert \lt 2\delta = 2(\frac{\epsilon}{2}) = \epsilon$
Therefore, $\lim\limits_{x \to 4} (2x-5)= 3$
