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Let's solve the given expression step by step. The expression is:

\[
\frac{2x - 3(x - z)}{z - 1}
\]
where \( x = 5 \) and \( z = 3 \).

### Step 1: Substitute the values of \( x \) and \( z \)
Substitute \( x = 5 \) and \( z = 3 \) into the expression:

\[
\frac{2(5) - 3(5 - 3)}{3 - 1}
\]

### Step 2: Simplify the terms
First, simplify inside the parentheses:

\[
5 - 3 = 2
\]

Now the expression becomes:

\[
\frac{2(5) - 3(2)}{3 - 1}
\]

### Step 3: Perform multiplication
Multiply the terms:

\[
2(5) = 10 \quad \text{and} \quad 3(2) = 6
\]

Now the expression is:

\[
\frac{10 - 6}{3 - 1}
\]

### Step 4: Simplify the numerator and denominator
Simplify the subtraction:

\[
10 - 6 = 4 \quad \text{and} \quad 3 - 1 = 2
\]

Now the expression is:

\[
\frac{4}{2}
\]

### Step 5: Final result
Divide:

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

So, the simplified value of the expression is \( 2 \).

---

Would you like further details on any of the steps? Here are five related questions you might want to explore:

1. How do you simplify algebraic fractions in general?
2. What are some common mistakes when substituting values into expressions?
3. How do parentheses affect the order of operations?
4. Can you explain the difference between simplifying and evaluating an expression?
5. How can simplifying fractions help in solving more complex algebraic equations?

**Tip**: Always simplify the expression inside parentheses first to avoid errors in calculation.

Evaluate and simplify the expression when x = 5 and z = 3: \( \frac{2x - 3(x - z)}{z - 1} \)

This step-by-step guide walks through the simplification of the algebraic expression \( \frac{2x - 3(x - z)}{z - 1} \) with x = 5 and z = 3. Learn key concepts in algebra such as substitution and simplification. Suitable for Grades 6-8.

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