The difference between six   times a number and nine   more than two   times the number.

Let's define the unknown number as \( x \).

The problem states two expressions:
1. "Six times a number" is \( 6x \).
2. "Nine more than two times the number" is \( 2x + 9 \).

The difference between these two expressions is:
\[
6x - (2x + 9)
\]
Now, distribute the negative sign:
\[
6x - 2x - 9 = 4x - 9
\]

So, the difference is \( 4x - 9 \).

Would you like further clarification or details?

Here are five related questions:
1. How do you solve for \( x \) when you have a specific equation involving this expression?
2. What if the number was negative? How would it change the difference?
3. Can you set the difference equal to a value and solve for \( x \)?
4. How do we apply distributive property when simplifying such expressions?
5. How does this translate to a word problem in a real-world context?

**Tip**: Always distribute the negative sign carefully when subtracting algebraic expressions to avoid common errors.

The difference between six times a number and nine more than two times the number.

Understand how to find the difference between six times a number and nine more than two times the number. This algebra problem uses key concepts like simplifying expressions and the distributive property. Suitable for Grades 6-8 students.

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