The expression you've given is:

\[
4^2 + 3 |4x - 9|
\]

Let's break it down:

1. \( 4^2 = 16 \), so the expression becomes:

\[
16 + 3 |4x - 9|
\]

2. The absolute value function, \( |4x - 9| \), means that whatever is inside the absolute value bars will always be non-negative. Hence, the final expression is:

\[
16 + 3 |4x - 9|
\]

This is simplified as far as it goes unless you want to evaluate it for a particular value of \( x \). Would you like to substitute a value for \( x \), or is this the final form you're looking for?

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Would you like more details or have any questions?

Here are 5 questions related to this expression:
1. What happens to the expression when \( x = 3 \)?
2. How does the absolute value affect different values of \( x \)?
3. Can you solve \( 16 + 3 |4x - 9| = 0 \)?
4. What are the properties of absolute value functions?
5. How does this expression change if the absolute value is removed?

**Tip:** Absolute values turn negative quantities into positive ones, affecting how equations and expressions behave.

This problem breaks down the expression 4^2 + 3|4x - 9|, covering exponentiation and absolute value. Learn how to simplify the expression step by step and explore how absolute values affect algebraic expressions. Suitable for students in Grades 8-10.

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