Match inequalities to their correct number line graphs in this solving and graphing inequalities worksheet.

Let's solve this step by step.

We are given 7 inequalities and 5 graphs. We need to match each inequality to its correct graph, but since there are more inequalities than graphs, some inequalities will not be used.

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Step 1: Understand how to interpret the graphs

On a number line:

- A closed circle (●) means the endpoint is included → use `≤` or `≥`
- An open circle (○) means the endpoint is not included → use `<` or `>`
- The arrow direction shows whether values go left (smaller) or right (larger)

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Step 2: Analyze each graph

Let’s label the graphs from top to bottom as Graph A to Graph E

#### Graph A
- Open circle at 4
- Arrow pointing left → values less than 4
- So: x < 4

> This matches inequality #5: x < 4

✔ Match: 5. x < 4 → Graph A

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#### Graph B
- Closed circle at 1
- Arrow pointing left → values less than or equal to 1
- So: x ≤ 1

> This matches inequality #1: x ≤ 1

✔ Match: 1. x ≤ 1 → Graph B

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#### Graph C
- Open circle at 3
- Arrow pointing right → values greater than 3
- So: x > 3

> This matches inequality #6: x > 3

✔ Match: 6. x > 3 → Graph C

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#### Graph D
- Open circle at -2
- Arrow pointing right → values greater than -2
- So: x > -2

> This matches inequality #4: x > -2

✔ Match: 4. x > -2 → Graph D

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#### Graph E
- Closed circle at 3
- Arrow pointing right → values greater than or equal to 3
- So: x ≥ 3

> This matches inequality #7: x ≥ 3

✔ Match: 7. x ≥ 3 → Graph E

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Now let’s check which inequalities are left unmatched:

- 1. x ≤ 1 → ✔ matched
- 2. x ≥ -2 → ✘ not matched
- 3. x ≤ 4 → ✘ not matched
- 4. x > -2 → ✔ matched
- 5. x < 4 → ✔ matched
- 6. x > 3 → ✔ matched
- 7. x ≥ 3 → ✔ matched

So only #2 and #3 are not matched — that’s expected since we have 5 graphs and 7 inequalities.

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Final Matching:

| Inequality | Graph |
|-----------|--------|
| 1. x ≤ 1 | Graph B |
| 4. x > -2 | Graph D |
| 5. x < 4 | Graph A |
| 6. x > 3 | Graph C |
| 7. x ≥ 3 | Graph E |

> Note: Inequalities 2 (x ≥ -2) and 3 (x ≤ 4) do not have corresponding graphs provided.

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Summary of Answers:

- 1. x ≤ 1 → Graph B
- 2. x ≥ -2 → No match
- 3. x ≤ 4 → No match
- 4. x > -2 → Graph D
- 5. x < 4 → Graph A
- 6. x > 3 → Graph C
- 7. x ≥ 3 → Graph E

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How to draw lines on the worksheet:

Draw a line from:
- 1 → Graph B
- 4 → Graph D
- 5 → Graph A
- 6 → Graph C
- 7 → Graph E

Leave 2 and 3 unconnected.

✔ All done!