From the image, we need to match the appropriate inequality symbol for each given situation based on the number lines.

Breakdown of each case:

1. Top line:

   • The number line shows a filled circle at $x = 0$, meaning $x$ includes $0$, and the arrow extends to the left. This represents $x \leq 0$.

2. Second line:

   • The number line shows an open circle at $x = -3$, meaning $x$ does not include $-3$, and the arrow extends to the right. This represents $x > -3$.

3. Third line:

   • The number line has a filled circle at $x = -2$ and an open circle at $x = 8$, meaning $x$ is in the range $-2 \leq x < 8$.

4. Fourth line:

   • The number line has a filled circle at $x = -5$ and a filled circle at $x = 6$, meaning $x$ is in the range $-5 \leq x \leq 6$.

Final Answers:

• $x \leq 0$
• $x > -3$
• $-2 \leq x < 8$
• $-5 \leq x \leq 6$

Would you like additional explanations or details?

Here are 5 related questions to enhance understanding:

1. How do we differentiate between strict ($<, >$) and non-strict ($\leq, \geq$) inequalities on a number line?
2. Why do open and closed circles represent different types of inequalities?
3. Can we have a situation where two inequalities are combined but one is strict and the other is non-strict?
4. How do you solve inequalities algebraically and verify the solution on a number line?
5. What happens if an inequality has no solution?

Tip: Always double-check the endpoints and direction of the number line to choose the correct inequality symbol!