What operations is happening to simplify this expression

∣
4
x
+
9
−
x
2
∣
3
3
∣
4x+9
​
−x
2
∣
​

To simplify the expression \(\left|\frac{4x + 9 - x^2}{3}\right|\), several operations are involved:

1. **Subtraction within the numerator:** The expression inside the absolute value involves subtracting \(x^2\) from \(4x + 9\).
   
   \[
   \text{Numerator: } 4x + 9 - x^2
   \]
   
2. **Division by 3:** The entire expression within the absolute value is divided by 3.
   
   \[
   \frac{4x + 9 - x^2}{3}
   \]

3. **Absolute value:** The result of the division is then enclosed within an absolute value, which ensures the expression is non-negative regardless of the value of \(x\).

   \[
   \left|\frac{4x + 9 - x^2}{3}\right|
   \]

Thus, the simplification process involves subtracting \(x^2\) from \(4x + 9\), dividing the result by 3, and then taking the absolute value of the entire expression.

Would you like a more detailed explanation or have any questions?

Here are 8 related questions you might find helpful:

1. What is the importance of the absolute value in mathematical expressions?
2. How does the order of operations affect the simplification process?
3. Can this expression be further simplified depending on the value of \(x\)?
4. How do you solve for \(x\) when such an expression equals a constant?
5. What happens if the absolute value is removed from the expression?
6. How can we interpret this expression graphically?
7. What are common mistakes when simplifying expressions involving absolute values?
8. How can this expression be used in a real-world context?

**Tip:** Always remember to apply the absolute value function last after performing all arithmetic operations inside the expression.

Explore how to simplify the expression |4x + 9 - x^2|/3 in algebra. Learn the steps involved, including subtraction within the numerator and division by 3. Suitable for students in Grades 7-9.

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