Answer
$\lim\limits_{x \to -3} (1-4x)= 13$
Work Step by Step
Let $\epsilon \gt 0$ be given.
Let $\delta = \frac{\epsilon}{4}$
Suppose that $\vert x-(-3) \vert \lt \delta$.
Note that $~~\vert x-(-3) \vert = \vert x+3 \vert$
Then:
$\vert (1-4x)-13 \vert = \vert -4x-12 \vert = \vert -4(x+3) \vert = 4\vert x+3 \vert \lt 4\delta = 4(\frac{\epsilon}{4}) = \epsilon$
Therefore, $\lim\limits_{x \to -3} (1-4x)= 13$
