https://file.aiquickdraw.com/mathbot/file/17265198287426x3ku3z7.jpg

The given equation is:

\[
\frac{6(4 - z)}{5} = -z
\]

Let's solve this step by step.

### Step 1: Distribute the 6 across the expression in the numerator
\[
\frac{6 \cdot 4 - 6 \cdot z}{5} = -z
\]
\[
\frac{24 - 6z}{5} = -z
\]

### Step 2: Eliminate the fraction by multiplying both sides of the equation by 5:
\[
24 - 6z = -5z
\]

### Step 3: Move all the terms involving \( z \) to one side:
\[
24 = -5z + 6z
\]
\[
24 = z
\]

### Final solution:
\[
z = 24
\]

Thus, the correct answer is \( \boxed{z = 24} \). The choice is A.

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:
1. How do you solve equations with fractions on both sides?
2. What happens if a fraction is multiplied incorrectly during solving?
3. How do you identify when there is no solution in an equation?
4. Can this problem have a different approach for solving?
5. How do you verify your solution is correct?

**Tip:** Always simplify equations step by step to avoid errors with fractions.

Learn how to solve the linear equation (6(4 - z))/5 = -z with a detailed step-by-step explanation. The solution involves distributing terms, eliminating fractions, and solving for the variable. This problem covers core algebraic concepts and is suitable for students in Grades 9-11.

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