https://file.aiquickdraw.com/mathbot/file/1729793309537blh6xblu.jpg

The expression to evaluate and simplify is:

\[
\frac{3b - 2(1 - b)}{a - 2}
\]
with the given values \(a = 3\) and \(b = 2\).

Let's break this down step by step:

### Step 1: Substitute \(a = 3\) and \(b = 2\) into the expression
\[
\frac{3(2) - 2(1 - 2)}{3 - 2}
\]

### Step 2: Simplify the numerator
\[
3(2) = 6
\]
and
\[
1 - 2 = -1
\]
so
\[
-2(-1) = 2.
\]

Thus, the numerator becomes:
\[
6 + 2 = 8.
\]

### Step 3: Simplify the denominator
\[
3 - 2 = 1.
\]

### Step 4: Final simplification
\[
\frac{8}{1} = 8.
\]

So, the value of the expression is:

\[
\boxed{8}.
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the result change if \(b = 1\) instead of 2?
2. Can you solve the same expression for \(a = 4\) and \(b = 3\)?
3. How can you rewrite the expression without parentheses and simplify it symbolically?
4. What happens to the expression when both \(a\) and \(b\) approach 0?
5. How does the expression change if \(a = b\)?

Tip: Always simplify the terms inside parentheses first to avoid mistakes in longer calculations.

Evaluate and simplify the expression when a = 3 and b = 2: (3b - 2(1 - b)) / (a - 2)

This problem involves simplifying an algebraic expression when a = 3 and b = 2. The solution includes substitution of values and step-by-step simplification. Suitable for students in Grades 7-9.

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