4.1 graphing inequalities | PDF - Free Printable

It looks like you've uploaded a worksheet with number line graphs and inequalities. Let's go through each problem step by step, solve it, and explain the reasoning.

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Problems 13–18: Graphing Inequalities

These problems show number lines with shaded regions and ask you to interpret or graph inequalities.

#### 13) –4 ≥ 2
This is not an inequality that can be graphed on a number line in the way shown. It's a false statement (since -4 is less than 2). But looking at the graph:
- The number line has a closed circle at 2 and shading to the left, meaning values ≤ 2.
- So this graph represents:
✔ x ≤ 2

But the given expression "–4 ≥ 2" is incorrect. Likely, the intended inequality is x ≤ 2, matching the graph.

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#### 14) 5.2 = 4
This is also a false statement (5.2 ≠ 4). But the graph shows:
- A closed circle at 4, shading to the right → x ≥ 4
- So the correct inequality should be:
✔ x ≥ 4

The given expression "5.2 = 4" is wrong. Probably meant to be x ≥ 4.

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#### 15) x ≤ 2
Graph: Closed circle at 2, shading to the left → includes 2 and all numbers less than 2
✔ This matches the inequality: x ≤ 2

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#### 16) x ≤ 5
Graph: Closed circle at 5, shading to the left → includes 5 and all numbers less than 5
✔ Matches: x ≤ 5

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#### 17) –5 > 8
False statement (–5 is not greater than 8). But the graph shows:
- Open circle at 8, shading to the left → x < 8
✔ So correct inequality: x < 8

Given expression is wrong; likely typo.

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#### 18) –2 > h
This is equivalent to: h < –2
Graph: Open circle at –2, shading to the left → h < –2
✔ Matches: h < –2

So the inequality should be written as: h < –2

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Write an inequality for each graph (19–24)

Now we interpret the graphs and write the correct inequality.

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#### 19)
Graph: Closed circle at 5, shading to the right
→ Includes 5 and all numbers greater than 5
✔ x ≥ 5

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#### 20)
Graph: Closed circle at –1, shading to the left
→ Includes –1 and all numbers less than –1
✔ p ≤ –1

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#### 21)
Graph: Open circle at –1, shading to the right
→ Does not include –1, but includes all numbers greater than –1
✔ x > –1

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#### 22)
Graph: Open circle at –5, shading to the left
→ Does not include –5, all numbers less than –5
✔ a < –5

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#### 23)
Graph: Open circle at 2, shading to the left
→ Does not include 2, all numbers less than 2
✔ p < 2

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#### 24)
Graph: Open circle at –5, shading to the right
→ Does not include –5, all numbers greater than –5
✔ n > –5

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✔ Final Answers:

| Problem | Correct Inequality |
|--------|--------------------|
| 13 | x ≤ 2 |
| 14 | x ≥ 4 |
| 15 | x ≤ 2 |
| 16 | x ≤ 5 |
| 17 | x < 8 |
| 18 | h < –2 |
| 19 | x ≥ 5 |
| 20 | p ≤ –1 |
| 21 | x > –1 |
| 22 | a < –5 |
| 23 | p < 2 |
| 24 | n > –5 |

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🔍 Explanation Summary:

- Closed circle: Value is included → use ≤ or ≥
- Open circle: Value is not included → use < or >
- Shading to the right: Values are greater than the point
- Shading to the left: Values are less than the point

Let me know if you'd like a visual explanation or help creating similar problems!