Express c in Inequalities: -9 < c < -1 on Number Line

Compound Inequalities with Number Line Visualization

c c is a negative number greater than -9 and less than -1 .

Write this as an expression using the number line below as an aid.

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

c c is a negative number greater than -9 and less than -1 .

Write this as an expression using the number line below as an aid.

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

2

Step-by-step solution

First, we'll mark the expression C<0 C < 0 on the number line:

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

Then we'll mark C>9 C > -9 :

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

Finally, we'll mark C<1 C < -1 :

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

Now we can see that the section marked in orange overlaps the expression:

-10-10-10-9-9-9-8-8-8-7-7-7-6-6-6-5-5-5-2-2-2-3-3-3-4-4-4-1-1-1000

The numbers that create the overlapping section are those from -9 to -1 and represent the expression in question:

9<c<1 -9 < c < -1

3

Final Answer

9<c<1 -9 < c < -1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Compound inequalities combine two conditions with AND logic
  • Technique: -9 < c means c > -9, and c < -1 gives -9 < c < -1
  • Check: Pick test value like c = -5: -9 < -5 < -1 is true ✓

Common Mistakes

Avoid these frequent errors
  • Writing separate inequalities instead of compound form
    Don't write c > -9 and c < -1 as separate statements = missed connection! This loses the relationship showing c must satisfy BOTH conditions simultaneously. Always combine into -9 < c < -1 to show the complete range.

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

Why can't I write this as c > -9 and c < -1?

+

While technically correct, the compound inequality -9 < c < -1 is much clearer! It shows the complete range in one expression and matches what you see on the number line.

How do I know which direction the inequality signs go?

+

Think of it as a chain: -9 is less than c, and c is less than -1. So we write -9 < c < -1, reading from smallest to largest value.

What does the number line show exactly?

+

The number line shows all values between -9 and -1 are highlighted. The open circles at -9 and -1 mean these endpoints are NOT included in the solution.

Could c equal -9 or -1?

+

No! The problem states c is greater than -9 and less than -1. This means c can be -8.9 or -1.1, but never exactly -9 or -1.

How can I check if my inequality is correct?

+

Pick any number between -9 and -1 (like -5 or -3) and verify: Is -9 < -5 < -1? Yes! Try a number outside the range like -10: Is -9 < -10 < -1? No, so -10 is correctly excluded.

What if I wrote -1 > c > -9 instead?

+

That's also correct mathematically! However, -9 < c < -1 is preferred because it follows the natural order from smallest to largest, making it easier to read and understand.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations