Answer
$x \lt 0 $ or $x \gt 6$
Work Step by Step
Let us consider the both inequalities.
$3x-1 \lt -1$
This can also be written as: $3x\lt -1+1$
or, $x \lt 0$
Now, $4-x \lt -2$
This can also be written as: $-x\lt -2-4$
or, $x \gt 6$
Therefore, our result is: $x \lt 0 $ or $x \gt 6$