is a negative number greater than -9 and less than -1 .
Write this as an expression using the number line below as an aid.
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is a negative number greater than -9 and less than -1 .
Write this as an expression using the number line below as an aid.
First, we'll mark the expression on the number line:
Then we'll mark :
Finally, we'll mark :
Now we can see that the section marked in orange overlaps the expression:
The numbers that create the overlapping section are those from -9 to -1 and represent the expression in question:
What is the distance between 0 and F?
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.
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.
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.
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.
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.
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.
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