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I have opened the image you uploaded. Let's solve the inequalities one by one and graph their solutions.

### 1. \( 5n + 17 > 12 \)

**Solution:**
\[
5n + 17 > 12 \\
5n > 12 - 17 \\
5n > -5 \\
n > -1
\]
The solution is \( n > -1 \). This will be represented on a number line with an open circle at \( -1 \), and the arrow pointing to the right.

---

### 2. \( 3p + 1 < 2p - 1 \)

**Solution:**
\[
3p + 1 < 2p - 1 \\
3p - 2p < -1 - 1 \\
p < -2
\]
The solution is \( p < -2 \). This will be represented with an open circle at \( -2 \), and the arrow pointing to the left.

---

### 3. \( 2(3x - 1) \geq 3(x - 1) \)

**Solution:**
\[
2(3x - 1) \geq 3(x - 1) \\
6x - 2 \geq 3x - 3 \\
6x - 3x \geq -3 + 2 \\
3x \geq -1 \\
x \geq -\frac{1}{3}
\]
The solution is \( x \geq -\frac{1}{3} \). This will be represented with a closed circle at \( -\frac{1}{3} \), and the arrow pointing to the right.

---

### 4. \( 3x - 2(x + 1) > 2x - 5 \)

**Solution:**
\[
3x - 2(x + 1) > 2x - 5 \\
3x - 2x - 2 > 2x - 5 \\
x - 2 > 2x - 5 \\
x - 2x > -5 + 2 \\
-x > -3 \\
x < 3
\]
The solution is \( x < 3 \). This will be represented with an open circle at \( 3 \), and the arrow pointing to the left.

---

### 5. \( 0 \leq x + 2 \leq 5 \)

**Solution:**
\[
0 \leq x + 2 \leq 5 \\
0 - 2 \leq x \leq 5 - 2 \\
-2 \leq x \leq 3
\]
The solution is \( -2 \leq x \leq 3 \). This will be represented with closed circles at \( -2 \) and \( 3 \), and the arrow between them.

---

### 6. \( 6 < 2(3 - m) < 18 \)

**Solution:**
\[
6 < 2(3 - m) < 18 \\
6 < 6 - 2m < 18
\]
First, solve the left side:
\[
6 < 6 - 2m \implies 6 - 6 < -2m \implies 0 < -2m \implies 0 > m
\]
Now solve the right side:
\[
6 - 2m < 18 \implies -2m < 12 \implies m > -6
\]
Thus, the solution is \( -6 < m < 0 \). This will be represented with open circles at \( -6 \) and \( 0 \), and the arrow between them.

---

Would you like more details on any of these steps or graphs?

Here are 5 related questions:
1. How do you solve compound inequalities like problem 5?
2. What is the difference between open and closed circles on a graph?
3. How would the solution change if a problem used \( \leq \) or \( \geq \)?
4. How do you handle negative coefficients when solving inequalities?
5. Can you explain how to graph inequalities on a number line?

**Tip:** When multiplying or dividing by a negative number in inequalities, always remember to flip the inequality sign!

Problems 1-8, solve each inequality. Graph the solution set.

Learn how to solve and graph inequalities such as 5n + 17 > 12, 3p + 1 < 2p - 1, and others with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving inequalities and graphing them on a number line. Suitable for students in Grades 6-8.

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