Solve the Inequality: Finding b When b > -6 with Number Line

Q: How do I know which values satisfy both conditions?

Look for the overlap on the number line! The solution includes only numbers that are both negative (less than 0) AND greater than -6, which gives us values between -6 and 0.

Q: Why isn't -6 included in the answer?

Because we need b > -6, which means strictly greater than -6. The symbol > doesn't include the boundary value, so -6 itself doesn't work.

Q: What's the difference between 0 > b > -6 and -6 < b < 0?

They're exactly the same! Both expressions describe numbers between -6 and 0. 0 > b > -6 reads from left to right: "0 is greater than b, and b is greater than -6."

Q: How do I read compound inequalities like this?

Break it into parts: 0 > b means "b is negative" and b > -6 means "b is greater than -6." Put them together: b must be negative but not too negative!

Q: Can I write this as b > -6 AND b < 0?

Yes! That's another correct way to write it. When you have AND between conditions, you can also write them as one compound inequality: -6

Compound Inequalities with Number Line Visualization

Select an expression which shows that b is a negative number greater than -6.

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Understand the problem

Select an expression which shows that b is a negative number greater than -6.

Step-by-step solution

First, we'll mark on the axis the expression $b < 0$

Then we'll mark on the axis the expression $b > -6$

We'll mark in orange the segment representing the requested expression:

$0 > b > -6$

Final Answer

$0 > b > -6$

Key Points to Remember

Essential concepts to master this topic

Rule: Combine two conditions using AND to find overlapping values
Technique: b < 0 AND b > -6 means -6 < b < 0
Check: Test b = -3: Is -3 negative AND greater than -6? ✓

Common Mistakes

Avoid these frequent errors

Reading inequality symbols backwards
Don't read b > -6 as "b is less than -6" = wrong direction! This reverses the entire solution set. Always read > as "greater than" and < as "less than" from left to right.

Practice Quiz

Test your knowledge with interactive questions

$$ 5 < -5 $$

FAQ

Everything you need to know about this question

How do I know which values satisfy both conditions?

Look for the overlap on the number line! The solution includes only numbers that are both negative (less than 0) AND greater than -6, which gives us values between -6 and 0.

Why isn't -6 included in the answer?

Because we need b > -6, which means strictly greater than -6. The symbol > doesn't include the boundary value, so -6 itself doesn't work.

What's the difference between 0 > b > -6 and -6 < b < 0?

They're exactly the same! Both expressions describe numbers between -6 and 0. 0 > b > -6 reads from left to right: "0 is greater than b, and b is greater than -6."

How do I read compound inequalities like this?

Break it into parts: 0 > b means "b is negative" and b > -6 means "b is greater than -6." Put them together: b must be negative but not too negative!

Can I write this as b > -6 AND b < 0?

Yes! That's another correct way to write it. When you have AND between conditions, you can also write them as one compound inequality: -6 < b < 0.

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