Solve the compound inequality: -5 < 2x + 3 ≤ 9.

Do the same operation on all three parts. Subtract $3$: $-8<2x\le6$. Divide by $2$ (positive, so no reversal): $-4<x\le3$, choice A. Choice D ($-8<x\le3$) forgets to divide the left part by $2$. Choice B ($-4<x\le6$) forgets to divide the right part by $2$. Choice C ($-1<x\le6$) adds $3$ instead of subtracting it, then divides. Test $x=3$: $2(3)+3=9$, which equals the upper bound, so $3$ is included, consistent with the symbol $\le$.