Identify the Inequality Using the Numerical Axis between -7 and -2

Q: How do I tell the difference between open and closed circles?

Open circles look like empty rings - they exclude the endpoint (use ). Closed circles are filled in - they include the endpoint (use ≤ or ≥).

Q: Why does the number line show -7 and 0 but the answer has -2?

Look carefully at the diagram! The major tick marks show -7, -2, and 0. The shaded interval goes from -7 to 0, not to -2. Always trace the actual highlighted region.

Q: What if I can't see the circles clearly?

Focus on whether the endpoint appears filled in (solid dot = closed = ≤ or ≥) or hollow (empty ring = open = ). This determines your inequality symbols.

Q: How do I write the inequality in the right order?

Read from left to right on the number line: \(-7 . This means x is greater than -7 AND less than or equal to 0.

Q: Can I write this as two separate inequalities?

Yes! $-7 means both \(-7 and \(x ≤ 0$. But the compound form is more concise.

Interval Notation with Open and Closed Endpoints

Which inequality is represented by the numerical axis below?

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Understand the problem

Which inequality is represented by the numerical axis below?

Step-by-step solution

To solve the problem and determine the inequality represented by the number line, follow these steps:

Examine the endpoints of the interval on the number line. At $-7$ , there is an open circle, indicating that $-7$ is not included in the interval.
At $0$ , there is a closed circle, indicating that $0$ is included in the interval.
This gives us the inequality for the interval: open at $-7$ ( $<$ ) and closed at $0$ ( $\leq$ ).

Therefore, the inequality represented by the number line is $-7 < x \leq 0$ .

This is consistent with option 1 in the provided choices. The inequality is represented by $-7 < x \leq 0$ .

Final Answer

$-7 < x ≤2$

Key Points to Remember

Essential concepts to master this topic

Circle Types: Open circle excludes point, closed circle includes point
Reading Method: Start from -7 (open) to 0 (closed) gives -7 < x ≤ 0
Verification: Check endpoints: -7 not included, 0 included in solution set ✓

Common Mistakes

Avoid these frequent errors

Confusing open and closed circles
Don't assume open circles mean ≤ and closed circles mean < = backwards inequality! This reverses which values are included or excluded. Always remember: open circles exclude the endpoint (< or >), closed circles include the endpoint (≤ or ≥).

Practice Quiz

Test your knowledge with interactive questions

Solve the following inequality:

$3x+4 \leq 10$

FAQ

Everything you need to know about this question

How do I tell the difference between open and closed circles?

Open circles look like empty rings - they exclude the endpoint (use < or >). Closed circles are filled in - they include the endpoint (use ≤ or ≥).

Why does the number line show -7 and 0 but the answer has -2?

Look carefully at the diagram! The major tick marks show -7, -2, and 0. The shaded interval goes from -7 to 0, not to -2. Always trace the actual highlighted region.

What if I can't see the circles clearly?

Focus on whether the endpoint appears filled in (solid dot = closed = ≤ or ≥) or hollow (empty ring = open = < or >). This determines your inequality symbols.

How do I write the inequality in the right order?

Read from left to right on the number line: $-7 < x ≤ 0$ . This means x is greater than -7 AND less than or equal to 0.

Can I write this as two separate inequalities?

Yes! $-7 < x ≤ 0$ means both $-7 < x$ and $x ≤ 0$ . But the compound form is more concise.

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Identify the Inequality Using the Numerical Axis between -7 and -2

Interval Notation with Open and Closed Endpoints

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I tell the difference between open and closed circles?

Why does the number line show -7 and 0 but the answer has -2?

What if I can't see the circles clearly?

How do I write the inequality in the right order?

Can I write this as two separate inequalities?

🌟 Unlock Your Math Potential

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