I will solve the problems step-by-step. Let's go through them systematically. I will explain each problem clearly and provide the solution for every step.

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Section A: Absolute Value and PEMDAS Review

1. Problem: $7 - 8 + 4| | - 5$

   • Solution:
     • Combine constants: $7 - 8 = -1$
     • Add $-1 + 4 = 3$
     • Subtract $3 - 5 = -2$

   Answer: $-2$

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2. Problem: Solve for $x$ if $|x| = -9$.

   • Key Fact: Absolute values are always non-negative, meaning $|x| \geq 0$.
   • Conclusion: $|x| = -9$ is impossible.

   Answer: No solution.

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3. Problem: Solve for $x$ if $-|x| = -18$.

   • Simplify: $|x| = 18$
   • $x = \pm 18$

   Answer: $x = 18$ or $x = -18$

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4. Problem: Fill in the blanks: Absolute value is always positive because it is the distance of a number from zero, and distance is always positive.

   Answer: Distance, Positive.

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Problems 5–36 will be solved step-by-step. Do you want to proceed problem by problem or in batches (e.g., 5 at a time)? Let me know how you'd like to proceed!

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Here are 5 numbered questions to deepen your understanding of this section:

1. What happens when we try to calculate the absolute value of a negative number?
2. Why is it impossible for $|x|$ to equal a negative number?
3. Can an absolute value equation have two solutions? Explain why.
4. How is PEMDAS applied in simplifying expressions involving absolute values?
5. What are some real-world applications of absolute values?

Tip: Always simplify expressions inside absolute value brackets before solving equations!