The problem in the image asks to identify the inequality that best represents the given graphs.

a. Graph Analysis:

• The arrow is pointing to the left, starting from -1 (open circle) and extending indefinitely towards negative infinity.
• This represents values less than -1, but not including -1 because of the open circle.

Thus, the inequality that represents this graph is: $x < -1$

b. Graph Analysis:

• The arrow starts from -5 (closed circle) and extends indefinitely to the right, towards positive infinity.
• This includes all values greater than or equal to -5, as indicated by the closed circle on -5.

Thus, the inequality that represents this graph is: $x \geq -5$

Would you like further clarification on these explanations? Here are five related questions to deepen your understanding:

1. How would the graph change if we had $x \leq -1$ instead of $x < -1$?
2. What would the inequality look like if the second graph (b) had an open circle at -5?
3. Can you graph the inequality $-3 < x \leq 4$ and explain the reasoning behind it?
4. How do you graph a compound inequality like $x > -2$ and $x \leq 3$?
5. How does the graph of $x \neq 0$ look, and how does it differ from $x = 0$?

Tip: Remember that an open circle on the graph means the point is not included (strict inequality), while a closed circle means it is included (inclusive inequality).