The task asks to graph the given inequalities on separate number lines. Let's address each inequality:

a. $x > 2$

1. On a number line, this inequality means all values of $x$ greater than 2.
2. To graph:
   • Draw an open circle at $x = 2$ (since $x$ does not include 2).
   • Shade the number line to the right of $x = 2$.

b. $x \leq 1$

1. On a number line, this inequality means all values of $x$ less than or equal to 1.
2. To graph:
   • Draw a closed circle at $x = 1$ (since $x$ can equal 1).
   • Shade the number line to the left of $x = 1$.

Would you like me to draw these graphs or clarify further? Let me know!

Related Questions:

1. What is the difference between $x > 2$ and $x \geq 2$ on a graph?
2. How do you determine where to shade for an inequality?
3. Why do we use open and closed circles in graphing inequalities?
4. Can you explain how to graph compound inequalities like $1 < x \leq 3$?
5. What does it mean when there is no solution to an inequality?

Tip:

When graphing inequalities, always pay attention to whether the inequality includes equality (closed circle) or not (open circle).