Answer
$5 \leq x \leq 10$
Work Step by Step
Let us consider the both inequalities.
$x \geq 3x-10$
This can also be written as: $x-3x \geq -10$
or, $x \geq 5$
Now, $3x-10 \leq 2x$
This can also be written as: $3x-2x \leq 10$
or, $x \leq 10$
Therefore, our result is: $5 \leq x \leq 10$