Let's simplify the given expression step by step:

The expression is:

$4(2x - 3) - 5(x + 2)$

1. First, distribute the constants:

   • Distribute $4$ to $2x - 3$: $4(2x) = 8x \quad \text{and} \quad 4(-3) = -12$ So, $4(2x - 3) = 8x - 12$.

   • Distribute $-5$ to $x + 2$: $-5(x) = -5x \quad \text{and} \quad -5(2) = -10$ So, $-5(x + 2) = -5x - 10$.

2. Now, combine the two parts: $8x - 12 - 5x - 10$

3. Combine like terms: $(8x - 5x) = 3x \quad \text{and} \quad (-12 - 10) = -22$

Thus, the simplified expression is: $3x - 22$

None of the provided options match exactly, but based on the work done, it seems there may be a mistake in the answer choices. The correct simplified expression is:

$3x - 22$.

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Do you need any further clarification on this? Here are some related questions:

1. How do you handle simplifications involving multiple variables?
2. What are the rules for distributing constants in an expression?
3. How would this expression change if one of the constants were negative?
4. Can you apply this method to more complex algebraic expressions?
5. How do you factor an expression like $3x - 22$?

Tip: Always distribute carefully, and combine like terms to simplify the expression properly.