Looks good. Though if you just want to present the proof, all that scrapwork isn't necessary and you simply start from "Given $\displaystyle \epsilon > 0$, Let $\displaystyle \delta = \min \left(1, \frac{\epsilon}{6}\right)$ ..." and so on.
One thing to note: $\displaystyle | x - 1| \ \Leftrightarrow \ -1 < x - 1 < 1 \ \Leftrightarrow \ 4 < x + 4 < 6 \ \Rightarrow |x+4| < {\color{red}6}$