https://file.aiquickdraw.com/mathbot/file/17294547660240qklzl9w.jpg

Let's solve the compound inequality given in the image:

\[
12 < x - 5 \leq 23
\]

### Step 1: Break the compound inequality into two parts:
1. \(12 < x - 5\)
2. \(x - 5 \leq 23\)

We solve each inequality separately.

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### Step 2: Solve \(12 < x - 5\)
Add 5 to both sides:
\[
12 + 5 < x \quad \Rightarrow \quad 17 < x \quad \text{or} \quad x > 17
\]

---

### Step 3: Solve \(x - 5 \leq 23\)
Add 5 to both sides:
\[
x - 5 + 5 \leq 23 + 5 \quad \Rightarrow \quad x \leq 28
\]

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### Step 4: Combine the results
The solution must satisfy both \(x > 17\) and \(x \leq 28\). Therefore, the solution is:

\[
17 < x \leq 28
\]

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### Step 5: Final answer
The solution set is:

\[
x \in (17, 28]
\]

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Do you have any questions or would you like further clarification?

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Here are 5 related questions:
1. How do you solve inequalities involving multiplication or division by negative numbers?
2. What is the difference between strict (\(<\)) and non-strict (\(\leq\)) inequalities?
3. How do you represent compound inequalities on a number line?
4. What are the properties of absolute value inequalities?
5. How do systems of inequalities differ from compound inequalities?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number.

Learn how to solve the compound inequality 12 < x - 5 ≤ 23 with a step-by-step breakdown. This problem covers algebraic concepts and properties of inequalities. Suitable for students in Grades 8-10.

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