https://file.aiquickdraw.com/mathbot/file/17261965627578vib4oog.jpg

The linear inequality given is:

\[
x - y \geq 3
\]

Let's solve and graph this step by step:

### Step 1: Rewrite the inequality
We first rearrange the inequality to express \( y \) in terms of \( x \):

\[
x - y \geq 3
\]

Subtract \( x \) from both sides:

\[
-y \geq 3 - x
\]

Now, multiply through by \(-1\) to solve for \( y \), remembering to reverse the inequality:

\[
y \leq x - 3
\]

### Step 2: Graph the boundary line
The boundary line is the equation \( y = x - 3 \). This line has a slope of 1 and a y-intercept of \(-3\). Since the inequality is \( y \leq x - 3 \), the graph will include the area below this line.

- **Solid Line**: Because the inequality is \( \leq \), we will draw a solid line to include points on the line \( y = x - 3 \).
- **Shaded Region**: The region below the line represents the solutions to the inequality \( y \leq x - 3 \).

### Step 3: Shading the region
Since the inequality is \( y \leq x - 3 \), we will shade the area below the line \( y = x - 3 \).

I can now visualize this inequality graph for you.

Should I generate the graph for this inequality?

### Related Questions:
1. How do we graph inequalities with different slopes?
2. What is the effect of switching the inequality symbol on the graph?
3. How can you check whether a point lies in the solution set of an inequality?
4. What changes occur if we use \( y \geq x - 3 \) instead of \( y \leq x - 3 \)?
5. How does the slope-intercept form help in graphing linear inequalities?

### Tip:
Always check which side of the boundary line you need to shade by testing a point, such as \( (0, 0) \), in the inequality.

Learn how to graph the linear inequality x - y >= 3. This step-by-step solution covers key algebraic concepts, including graphing linear inequalities and understanding slope-intercept form. Suitable for students in Grades 8-10.

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