Solve the compound inequality.

−2<2x+2≤9

Enter the exact answer in interval notation.

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:

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

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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.

Solve the compound inequality.

−2 < 2x + 2 ≤ 9

Enter the exact answer in interval notation.

Learn how to solve the compound inequality −2 < 2x + 2 ≤ 9 and express the solution in interval notation. This problem demonstrates key algebraic concepts in solving and combining inequalities, suitable for students in Grades 8-10.

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