To solve the compound inequality:

$-2 < 2x + 2 \leq 9$

we can break it down and solve each part separately.

Step 1: Solve $-2 < 2x + 2$

1. Subtract 2 from both sides: $-4 < 2x$
2. Divide by 2: $-2 < x$

So, this part of the inequality gives us: $x > -2$

Step 2: Solve $2x + 2 \leq 9$

1. Subtract 2 from both sides: $2x \leq 7$
2. Divide by 2: $x \leq \frac{7}{2}$

So, this part of the inequality gives us: $x \leq \frac{7}{2}$

Step 3: Combine the results

The solution to the compound inequality is the intersection of $x > -2$ and $x \leq \frac{7}{2}$. In interval notation, this is:

$(-2, \frac{7}{2}]$

---

Let me know if you want more details or have questions. Here are 5 related questions for practice:

1. Solve the compound inequality $3 < 5x - 2 \leq 13$.
2. Express the solution of $1 < 3x + 1 \leq 10$ in interval notation.
3. Find the solution of the inequality $-4 < 4x - 6 \leq 8$.
4. Solve the inequality $-5 \leq 2x + 3 < 9$.
5. Determine the interval for which $2 < 4x + 6 \leq 14$ holds true.

Tip: Always isolate the variable step-by-step to simplify compound inequalities.