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The expression you need to simplify is:

\[
(-2x + 3) - (2x - 2)
\]

Let’s go step by step to simplify it:

1. **Distribute the negative sign** to the second set of parentheses:
\[
(-2x + 3) - (2x - 2) = -2x + 3 - 2x + 2
\]

2. **Combine like terms**:
   - Combine the \(x\)-terms: \(-2x - 2x = -4x\)
   - Combine the constant terms: \(3 + 2 = 5\)

So, the simplified expression is:

\[
-4x + 5
\]

Would you like any further explanation?

Here are 5 related questions you might consider:
1. How would the process change if there were different variables?
2. What happens if you add fractions within parentheses instead of integers?
3. How do you simplify expressions with more complex polynomials?
4. How do you handle subtraction when parentheses include exponents?
5. What happens when you introduce multiple variables, like \(x\) and \(y\)?

**Tip**: Always distribute the negative sign across all terms inside the parentheses before combining like terms.

Perform the indicated operations and simplify: (-2x + 3) - (2x - 2)

Learn how to simplify the algebraic expression (-2x + 3) - (2x - 2) by applying the distributive property and combining like terms. This problem covers key algebraic concepts suitable for students in Grades 7-9.

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