There are two ways you could approach this.
The first is to solve each inequality separately and see which one ends up equal to x ≥ -1.
Another and faster option is to test 0 in each inequality, because 0 is in the solution set and 0 is easy to work with. (You could do this for any value in the solution set.)
A: Is 4(0) + 3 > 7 true? No. 3 > 7 is false. This eliminates A.
B. Is 0/3 - 2 ≥ 2 true? No. -2 ≥ 2 is false. This eliminates B.
C. Is -2(0) - 3 ≤ -1 true? Yes. -3 ≤ -1 is false. We cannot eliminate C.
D. Is 0 + 5 < 4 true? No. 5 < 4 is false. This eliminates D.
So based on using x=0, the only possible solution is C.
You can double check this by solving 2x - 3 ≤ -1 for x:
-2x - 3 ≤ -1
-2x ≤ 2 (by adding 3 to both sides)
Now when you divide by -2 to solve for x, remember to flip the inequality.
-2x ≤ 2
x ≥ -1
So this confirms that C is correc.