Let's simplify the given expression step by step:

Expression:

$3 - (2 - 4x) + 9$

1. Distribute the negative sign through the parentheses:
   $3 - 2 + 4x + 9$

2. Combine like terms (constants):
   $(3 - 2 + 9) + 4x = 10 + 4x$

Final Answer:

$10 + 4x$

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Would you like further details or have any questions?
Here are five related questions to explore further:

1. What are like terms, and how are they combined in algebra?
2. How do parentheses affect algebraic expressions, and how do you simplify them?
3. What does distributing a negative sign mean in an equation?
4. Can this expression be rewritten in terms of a specific variable value (e.g., $x = 2$)?
5. How would the result change if there were additional parentheses or operations?

Tip: Always simplify expressions by handling parentheses and combining like terms first to avoid errors.