To solve the inequality \(2x + 3y > -5\), we can represent it graphically or analyze it algebraically. 

### Step-by-step process:
1. Rewrite the inequality to express it as an equation first:
   \[
   2x + 3y = -5
   \]
   This is the boundary line for the inequality, which we'll use to determine the solution region.

2. **Find the intercepts**:
   - When \(x = 0\), solve for \(y\):
     \[
     3y = -5 \quad \Rightarrow \quad y = -\frac{5}{3}
     \]
   - When \(y = 0\), solve for \(x\):
     \[
     2x = -5 \quad \Rightarrow \quad x = -\frac{5}{2}
     \]

3. **Graph the boundary line**:
   - Plot the intercepts at \((0, -\frac{5}{3})\) and \((- \frac{5}{2}, 0)\).
   - Draw the line. This line represents the equation \(2x + 3y = -5\).
   - Since the original inequality is strict (using \(>\)), the line should be dashed, indicating that the points on the line are **not** included in the solution.

4. **Determine the region**:
   - Select a test point (such as the origin, \((0, 0)\)).
   - Substitute \((0, 0)\) into the inequality:
     \[
     2(0) + 3(0) > -5 \quad \Rightarrow \quad 0 > -5
     \]
   - This is true, so the region containing the origin is the solution set for the inequality.

### Final Answer:
The solution to \(2x + 3y > -5\) is the region above the dashed line \(2x + 3y = -5\).

Would you like a more detailed graphical explanation?

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Here are 5 related questions to explore further:
1. How do you solve inequalities with absolute values?
2. What happens when an inequality involves quadratic terms?
3. How do systems of inequalities get solved graphically?
4. How does reversing an inequality change its solution set?
5. What are the methods to solve inequalities involving logarithms?

**Tip:** Always remember to reverse the inequality symbol when multiplying or dividing by a negative number!

This guide explains how to solve the linear inequality 2x + 3y > -5 using algebraic methods and graphical representation. Learn the steps to find intercepts, plot the boundary line, and determine the solution region. Suitable for students in Grades 9-11.

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