The given inequality is:

\[
3x + y > -7
\]

This inequality represents a half-plane on the coordinate plane. To graph or analyze this inequality, we can follow these steps:

### Step 1: Convert to an equation
To understand the boundary of the inequality, first convert it into an equation:
\[
3x + y = -7
\]
This is the equation of a line, which forms the boundary between the solutions of the inequality and the non-solutions.

### Step 2: Find the intercepts
- **x-intercept**: Set \(y = 0\), and solve for \(x\):
  \[
 

This guide shows how to solve and graph the linear inequality 3x + y > -7. The process includes finding the boundary line and determining the solution region. Suitable for students in Grades 8-10.

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