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!

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!