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To graph the inequality \( x \leq 3 \):

1. **Plot the boundary line**: The boundary for this inequality is the line \( x = 3 \). This line will be **solid** because the inequality includes equality (≤). A solid line indicates that the points on the line itself are part of the solution.

   - Draw a vertical line passing through \( x = 3 \).

2. **Shade the correct region**: Since the inequality is \( x \leq 3 \), you will shade the region **to the left** of the line \( x = 3 \), because this region includes all values where \( x \) is less than or equal to 3.

Steps:
- Plot the vertical line at \( x = 3 \) and make it solid.
- Shade the region to the left of the line.

Let me know if you'd like more details or clarification!

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Here are five related questions to expand your understanding:

1. How would the graph change if the inequality were \( x < 3 \)?
2. How can you determine which side of the boundary to shade for other inequalities like \( y > 2x \)?
3. What is the significance of using a solid line versus a dashed line in inequalities?
4. How would you graph a compound inequality like \( -2 \leq x \leq 4 \)?
5. What happens to the shaded region when graphing inequalities with both \( x \) and \( y \)?

**Tip**: Always check whether the inequality includes equality (≤ or ≥), as this determines whether the boundary line is solid or dashed!

Graph the inequality x ≤ 3 and shade the appropriate region.

Learn how to graph the inequality x ≤ 3 by drawing the boundary at x = 3 with a solid line and shading the region where x is less than or equal to 3. Ideal for students in Grades 6-8, this step-by-step guide covers key concepts of graphing and inequalities.

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