Answer
$x \gt 3$
Work Step by Step
Let us consider the both inequalities.
$2x-5 \geq 3$
This can also be written as: $2x\geq 3+5$
or, $x \geq 4$
Now, $3-x \lt 0$
This can also be written as: $-x\lt 0-4$
or, $x \gt 3$
Therefore, our result is: $x \gt 3$