Let's solve the expression step by step:

\[
2 - 3(4 - 2) + \frac{3}{2}
\]

1. First, simplify inside the parentheses:

\[
4 - 2 = 2
\]

Now the expression becomes:

\[
2 - 3(2) + \frac{3}{2}
\]

2. Multiply \(3 \times 2 = 6\):

\[
2 - 6 + \frac{3}{2}
\]

3. Subtract \(2 - 6 = -4\):

\[
-4 + \frac{3}{2}
\]

4. Convert \(-4\) to a fraction with denominator 2:

\[
-4 = \frac{-8}{2}
\]

Now the expression becomes:

\[
\frac{-8}{2} + \frac{3}{2}
\]

5. Add the fractions:

\[
\frac{-8 + 3}{2} = \frac{-5}{2}
\]

Thus, the result is:

\[
\boxed{-\frac{5}{2}}
\]

Would you like a detailed breakdown of any step? Here are some questions to further explore:

1. What happens if the fraction was different in the original expression?
2. How would the result change if the signs inside the parentheses were flipped?
3. Can you explain how to handle negative fractions in addition and subtraction?
4. How do you multiply fractions by whole numbers?
5. What are some common mistakes made in simplifying such expressions?

**Tip**: Always handle parentheses first according to the order of operations (PEMDAS).

Explore how to solve the arithmetic expression 2 - 3(4 - 2) + 3/2 with detailed steps. This solution emphasizes key concepts such as order of operations (PEMDAS), multiplying whole numbers, and adding fractions. Ideal for students in Grades 6-8.

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