Lesson: Representing Inequalities on a Number Line | Oak National ... - Free Printable

The image shows three number lines labeled A, B, and C, each representing a different interval on the real number line. We need to interpret what each graph represents in terms of inequalities.

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Understanding the Symbols:

- A closed circle (●) means the endpoint is included in the interval.
- An open circle (○) means the endpoint is excluded.
- Arrows indicate that the interval continues indefinitely in that direction.

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Let’s analyze each one:

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A:

- Closed circle at -2 → includes -2
- Open circle at 2 → does not include 2
- Line connects them → interval between -2 and 2

So this represents:
> $$
> -2 \leq x < 2
> $$

This is a closed-open interval: $[-2, 2)$

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B:

- Closed circle at -2 → includes -2
- Arrow going left → all numbers less than or equal to -2
- Open circle at 2 → does not include 2
- Arrow going right → all numbers greater than 2

So this is two separate parts:
- $x \leq -2$
- $x > 2$

Combined:
> $$
> x \leq -2 \quad \text{or} \quad x > 2
> $$

In interval notation: $(-\infty, -2] \cup (2, \infty)$

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C:

- Open circle at -2 → does not include -2
- Arrow going left → all numbers less than -2
- Closed circle at 2 → includes 2
- Arrow going right → all numbers greater than or equal to 2

So:
- $x < -2$
- $x \geq 2$

Combined:
> $$
> x < -2 \quad \text{or} \quad x \geq 2
> $$

In interval notation: $(-\infty, -2) \cup [2, \infty)$

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✔ Summary:

| Option | Inequality | Interval Notation |
|--------|------------|-------------------|
| A | $-2 \leq x < 2$ | $[-2, 2)$ |
| B | $x \leq -2$ or $x > 2$ | $(-\infty, -2] \cup (2, \infty)$ |
| C | $x < -2$ or $x \geq 2$ | $(-\infty, -2) \cup [2, \infty)$ |

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If your task was to identify which one matches a given inequality, please provide that inequality. Otherwise, this is the full interpretation of the three graphs.

Let me know if you'd like to compare them or solve a specific problem involving these!