The compound inequality is $x \leq 2$ or $x > 5$. To interpret this, we need to understand:

1. $x \leq 2$ means that the solution includes all values less than or equal to 2, which would be shown with a closed circle at 2 and a line extending to the left.
2. $x > 5$ means all values greater than 5, which would be shown with an open circle at 5 and a line extending to the right.

Now let's analyze the options:

• Option 1: This shows a line extending left from 2 (with a closed circle at 2) and a line extending right from 5 (with an open circle at 5), which matches the given inequality.
• Option 2: This is incorrect because both circles are filled, suggesting $x \geq 5$, not $x > 5$.
• Option 3: This is incorrect because the circle at 5 is closed, which implies $x \geq 5$ instead of $x > 5$.
• Option 4: This is incorrect because it represents the solution for $2 \leq x \leq 5$, which is a different range.
• Option 5: This is incorrect because there is no line extending from 5, and it misrepresents the inequality.
• Option 6: This is incorrect because both ends have closed circles, which would mean $x \geq 5$.

The correct answer is Option 1.

Would you like more details or have any further questions? Here are 5 related questions to explore this further:

1. How do you graph compound inequalities that use "and" instead of "or"?
2. What is the difference between open and closed circles on a number line?
3. How do you write inequalities that include absolute values?
4. What types of problems require compound inequalities?
5. Can you convert compound inequalities into interval notation?

Tip: Remember that closed circles on a graph represent values included in the solution, while open circles indicate values that are excluded.