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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Step-by-step video solution

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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

All negative numbers appear on the number line to the left of the number 0.

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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