To solve the inequality \(5x + 4y < -16\), we can analyze it in different ways depending on what you're looking for. Here's a basic outline:

### 1. **Finding the Boundary Line:**
   - First, we convert the inequality into an equation to find the boundary line:
   \[
   5x + 4y = -16
   \]
   - This represents a straight line in the coordinate plane.

### 2. **Graphing the Line:**
   - To graph the line, find the intercepts:
     - **x-intercept:** Set \(y = 0\) and solve for \(x\):
       \[
       5x = -16 \implies x = -\frac{16}{5}
       \]
     - **y-intercept:** Set \(x = 0\) and solve for \(y\):
       \[
       4y = -16 \implies y = -4
       \]
   - Plot these points and draw the line through them.

### 3. **Shading the Appropriate Region:**
   - Since the inequality is \(5x + 4y < -16\), we shade the region below the line because we are interested in the values that make the expression less than \(-16\).

### 4. **Test a Point:**
   - To ensure you've shaded the correct region, you can test a point not on the line (usually the origin \((0, 0)\)) in the original inequality:
     - Substitute \(x = 0\) and \(y = 0\):
       \[
       5(0) + 4(0) = 0
       \]
     - Since \(0 > -16\), the origin is not part of the solution set, confirming that the correct region is below the line.

### 5. **Solution Set:**
   - The solution to the inequality is the region below the line \(5x + 4y = -16\), excluding the line itself.

Would you like more details on graphing or solving this inequality?

Here are five related questions you might find useful:
1. How do you solve a system of linear inequalities?
2. What does the solution set of an inequality represent geometrically?
3. How do you determine if a point is within the solution set of an inequality?
4. Can you graph an inequality with two variables?
5. How do linear inequalities differ from linear equations?

**Tip:** When graphing inequalities, always use a dashed line for "<" or ">" and a solid line for "≤" or "≥".

Learn how to solve the inequality 5x + 4y < -16 with a step-by-step graphical explanation. Understand the process of graphing linear equations and shading regions based on inequality signs. Suitable for students in Grades 7-9 studying algebra and graphing linear equations.

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