Answer
Divergent
Work Step by Step
Let
\[I=\int_{-\infty}^{0}\frac{1}{3-4x}dx\;\;\;\ldots(1)\]
\[I=\lim_{t\rightarrow -\infty}\int_{t}^{0}\frac{1}{3-4x}dx\;\;\;\ldots(2)\]
\[I=\lim_{t\rightarrow -\infty}\left[-\frac{1}{4}\ln|3-4x|\right]_{t}^{0}\]
\[I=\lim_{t\rightarrow -\infty}\left[-\frac{1}{4}\ln 3+\frac{1}{4}\ln|3-4t|\right]\]
\[I=\infty\]
Since limit on R.H.S. of (2) does not exist
So given improper integral (1) is divergent.
