Matching inequalities to their number line graphs on a math worksheet.

Let’s go step by step to match each inequality with its correct graph.

We need to remember:
- A closed circle (●) means the number is included → used for ≤ or ≥
- An open circle (○) means the number is NOT included → used for < or >
- The arrow shows which direction the numbers go that satisfy the inequality.

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Let’s look at each inequality and find its matching graph:

1. x ≤ 1
→ Includes 1, so closed circle at 1.
→ Arrow goes to the left (numbers less than 1).
Look at the graphs:
The second graph from top has a closed circle at 1 and arrow going left to -5. ✔ That matches.

2. x ≥ -2
→ Includes -2, so closed circle at -2.
→ Arrow goes to the right.
Check graphs: None have closed circle at -2? Wait — let’s check again.
Actually, none of the graphs show a closed circle at -2. So maybe this one doesn’t have a match? But instructions say “you will NOT use all inequalities” — so some won’t be matched. We’ll come back if needed.

Wait — let’s list all graphs first to avoid confusion.

Graphs (from top to bottom):

A. Number line from 1 to 5, open circle at 4, arrow left → represents x < 4
B. Number line from -5 to 5, closed circle at 1, arrow left → x ≤ 1
C. Number line from 0 to 10, open circle at 3, arrow right → x > 3
D. Number line from -8 to 8, open circle at -2, arrow right → x > -2
E. Number line from -6 to 6, closed circle at 3, arrow right → x ≥ 3

Wait — I think I miscounted. Let me label them clearly as they appear in the image (top to bottom on right side):

Graph 1 (top):
Number line labeled 1 to 5, open circle at 4, arrow pointing left → This is x < 4

Graph 2:
Number line labeled -5 to 5, closed circle at 1, arrow pointing left → This is x ≤ 1

Graph 3:
Number line labeled 0 to 10, open circle at 3, arrow pointing right → This is x > 3

Graph 4:
Number line labeled -8 to 8, open circle at -2, arrow pointing right → This is x > -2

Graph 5 (bottom):
Number line labeled -6 to 6, closed circle at 3, arrow pointing right → This is x ≥ 3

Now match inequalities:

1. x ≤ 1 → Graph 2 (closed circle at 1, arrow left) ✔

2. x ≥ -2 → Need closed circle at -2, arrow right. None of the graphs have that. So no match → skip

3. x ≤ 4 → Need closed circle at 4, arrow left. Graph 1 has OPEN circle at 4 → not match. No other graph has 4 as endpoint. So no match → skip

4. x > -2 → Open circle at -2, arrow right → Graph 4 ✔

5. x < 4 → Open circle at 4, arrow left → Graph 1 ✔

6. x > 3 → Open circle at 3, arrow right → Graph 3 ✔

7. x ≥ 3 → Closed circle at 3, arrow right → Graph 5 ✔

So we have matches for:

1 → Graph 2
4 → Graph 4
5 → Graph 1
6 → Graph 3
7 → Graph 5

Inequalities 2 and 3 have no matching graphs — which is fine per instructions.

Final Answer:

1. x ≤ 1 → Graph 2
2. x ≥ -2 → (no match)
3. x ≤ 4 → (no match)
4. x > -2 → Graph 4
5. x < 4 → Graph 1
6. x > 3 → Graph 3
7. x ≥ 3 → Graph 5