Which equation is equivalent to the given equation?

Let's revisit the problem to identify which equation is equivalent to the given one:

### Given Equation:
\[
-4(z - 5) + 8z = 9z - 3
\]

### Step 1: Distribute \(-4\) to the terms inside the parentheses.
\[
-4 \cdot z + (-4) \cdot (-5) + 8z = 9z - 3
\]
\[
-4z + 20 + 8z = 9z - 3
\]

### Step 2: Combine like terms on the left-hand side.
\[
(-4z + 8z) + 20 = 9z - 3
\]
\[
4z + 20 = 9z - 3
\]

### Step 3: Subtract \(9z\) from both sides to move all terms involving \(z\) to one side.
\[
4z - 9z + 20 = -3
\]
\[
-5z + 20 = -3
\]

### Step 4: Subtract 20 from both sides to isolate the term involving \(z\).
\[
-5z = -3 - 20
\]
\[
-5z = -23
\]

### Step 5: Simplify the equation.
\[
5z = 23 \quad \text{or equivalently} \quad -5z = 23
\]

### Conclusion:
The equation that is equivalent to the given equation is:

**Option C: \(-5z = -23\)**

This matches with option C.

Would you like more details or have any questions?

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### Related Questions:
1. How do you isolate the variable \(z\) in an equation?
2. Why is it important to combine like terms in algebra?
3. How do you handle negative coefficients when solving equations?
4. What are the steps to check if two equations are equivalent?
5. How do you distribute a negative number across a binomial?
6. What are the possible mistakes when subtracting terms from both sides of an equation?
7. How can equivalent equations have different forms but represent the same relationship?
8. How do you verify the solution to a linear equation?

### Tip:
Always double-check each step when simplifying equations, especially when dealing with negative signs, to avoid simple errors that can lead to incorrect answers.

Explore which equation is equivalent to the given equation -4(z - 5) + 8z = 9z - 3 with detailed step-by-step solutions. This problem involves algebraic concepts like combining like terms and isolating variables. Suitable for Grades 7-9.

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