Choice B is the correct answer. Finding integer solutions requires solving first, then identifying appropriate values.

1. Multiply by 2: $2 \cdot \frac{x+5}{2} > 2 \cdot 4$, giving $x + 5 > 8$
2. Subtract 5: $x > 3$
3. Integer interpretation: $x$ must be GREATER than 3, so smallest integer is 4

?�� Strategic Tip: For strict inequalities ($>$ or $<$), the boundary value is excluded, so round to the next integer in the appropriate direction.

Choice A is incorrect because$x = 3$ is the boundary value and does NOT satisfy $x > 3$ (strict inequality). Choice C is incorrect because while 5 satisfies the inequality, it's not the SMALLEST integer that does. Choice D is incorrect because 6 satisfies it but is larger than the smallest valid integer.