Find the solution set of the inequality: $4x + 3 \geq 2x + 17$ and $3x - 5 < -2$.

(NONE) We have $4x + 3 \geq 2x + 17$.
$\therefore 4x - 2x \geq 17 - 3$
$\therefore 2x \geq 14$
$\therefore x \geq 7$
$...(i)$
Now,we have $3x - 5 < -2$.
$\therefore 3x < -2 + 5$
$\therefore 3x < 3$
$\therefore x < 1$
$...(ii)$
From $(i)$ and $(ii)$,we need to find the values of $x$ that satisfy both $x \geq 7$ and $x < 1$ simultaneously.
Since there is no real number $x$ that is both greater than or equal to $7$ and less than $1$,the solution set is the empty set,denoted by $\emptyset$.