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The problem presents a system of linear inequalities:

\[
\begin{cases}
x \geq -2 \\
x - 2y - 2 < 0
\end{cases}
\]

Let's analyze and solve this system by finding the region of the coordinate plane that satisfies both inequalities.

### Step 1: Solve each inequality separately

1. **First inequality:** \( x \geq -2 \)
   - This inequality represents a vertical line at \( x = -2 \).
   - Since \( x \geq -2 \), we shade the region to the right of this line.

2. **Second inequality:** \( x - 2y - 2 < 0 \)
   - Rearrange this inequality to make it easier to interpret:
     \[
     x - 2y < 2
     \]
     Then, isolate \( y \):
     \[
     -2y < 2 - x
     \]
     Divide by \(-2\) (remember to reverse the inequality sign):
     \[
     y > \frac{x}{2} - 1
     \]
   - This inequality represents a line with a slope of \( \frac{1}{2} \) and a y-intercept at \(-1\). Since \( y > \frac{x}{2} - 1 \), we shade the region above this line.

### Step 2: Determine the Solution Region
The solution region is where the shaded areas for both inequalities overlap:
- The region to the right of \( x = -2 \).
- The region above the line \( y = \frac{x}{2} - 1 \).

Would you like a more detailed graph of the solution region or have any questions?

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### Related Questions
1. How do you graph a linear inequality on a coordinate plane?
2. What does it mean to "reverse the inequality sign" when dividing by a negative number?
3. How can we verify if a point is within the solution region for a system of inequalities?
4. What is the difference between strict (\(<\), \(>\)) and non-strict (\(\leq\), \(\geq\)) inequalities?
5. How can systems of inequalities represent feasible regions in optimization problems?

### Tip
When working with inequalities, always double-check the direction of the inequality, especially after dividing by a negative value, as this reverses the inequality direction.

Mr. Benjamin gave his students the following system of linear inequalities:
\[
\begin{cases}
x \geq -2 \\
x - 2y - 2 < 0
\end{cases}
\]

Explore how to solve a system of linear inequalities with x ≥ -2 and x - 2y - 2 < 0. This solution includes steps for solving each inequality individually, shading regions on the coordinate plane, and finding the overlapping solution region. Ideal for students in Grades 9-11 learning about systems of inequalities.

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