The expression you provided is:

\[
\left| -8x + \frac{9}{4} \right|
\]

This represents the absolute value of \(-8x + \frac{9}{4}\), which means that the expression inside the absolute value will always be non-negative. More specifically:

\[
\left| -8x + \frac{9}{4} \right| = 
\begin{cases} 
  -8x + \frac{9}{4}, & \text{if } -8x + \frac{9}{4} \geq 0 \\
  -(-8x + \frac{9}{4}) = 8x - \frac{9}{4}, & \text{if } -8x + \frac{9}{4} < 0
\end{cases}
\]

Would you like me to evaluate this for specific values of \(x\), or solve an equation involving this expression? Let me know how you'd like to proceed.

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Here are five relative questions:

1. How do you want to solve the absolute value expression for different values of \(x\)?
2. Should we find when the expression inside the absolute value is positive or negative?
3. Are you looking for a specific solution or graph for this expression?
4. Would you like to know more about how absolute value functions behave graphically?
5. Would you like a step-by-step guide to solving absolute value equations?

**Tip**: The absolute value of an expression can be thought of as a "reflection" of negative outputs into positive ones, which is useful in solving and graphing functions.

Explore how to solve the absolute value expression | -8x + 9/4 |. This solution breaks down the properties of absolute value functions and provides step-by-step instructions on handling expressions with absolute values in algebra. Ideal for students in Grades 8-10.

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