The only solution to the inequality 3≤z is z=3.Therefore , z=3 is correct.
The inequality shown in the image is 3≤z. The only answer choice that satisfies this inequality is z=3.
Therefore the only solution is z=3.
In order to arrive at the answer, we can first rewrite the inequality to isolate z.
Subtracting 3 from both sides of the inequality, we get z≥0.
We can see from the answer choices that only z=3 satisfies this inequality.
Therefore, z=3 is the only solution.
The other answer choices can be eliminated as follows:
z=1: Substituting 1 for z in the inequality, we get 3≤1.
This is clearly not true, so z=1 is not a solution.
z=7: Substituting 7 for z, we get 3≤7.
This is true, but the question asks for the smallest solution. Since 3 is also a solution and it is smaller than 7, z=7 is not the smallest solution.
7 =11: Substituting 11 for z, we get 3≤11.
This is true, but as with z=7, it is not the smallest solution.
Therefore, the only solution to the inequality 3≤z is z=3.