To graph the inequality $x \leq 1$, follow these steps:

1. Draw the vertical line $x = 1$:

   • This line is vertical because it represents all points where the $x$-coordinate is 1.
   • Use a solid line for this boundary since the inequality includes $x = 1$ (indicated by "≤").

2. Shade the region to the left of the line:

   • Since the inequality is $x \leq 1$, shade the entire region to the left of the line, where $x$ is less than or equal to 1.

The final graph will show a solid vertical line at $x = 1$ and shading to the left of this line.

Would you like to see a visual representation of this graph, or do you have any questions?

Here are some related questions:

1. How would the graph change if the inequality were $x < 1$?
2. What would the graph look like for $x \geq 1$?
3. How would you graph a compound inequality, like $-2 \leq x \leq 1$?
4. Can you explain how to graph a similar inequality in two variables, like $x + y \leq 2$?
5. How does the shading differ when graphing $y \geq 1$ instead of $x \leq 1$?

Tip: Always use a solid line for "≤" or "≥" inequalities and a dashed line for "<" or ">".