To solve the equation \(12 - 6z = 10 - 5z\), we will isolate the variable \(z\) on one side. Here are the steps:

### Step-by-Step Solution

1. **Add \(5z\) to both sides** to move all terms involving \(z\) to one side:

\[
12 - 6z + 5z = 10 - 5z + 5z
\]

This simplifies to:

\[
12 - z = 10
\]

2. **Subtract 12 from both sides** to move the constant terms to the other side:

\[
12 - 12 - z = 10 - 12
\]

This simplifies to:

\[
-z = -2
\]

3. **Multiply both sides by -1** to solve for \(z\):

\[
z = 2
\]

### Solution

The value of \(z\) is \(2\).

Would you like more details, or do you have any questions?

### Related Questions

1. What is the solution to \(4x + 7 = 3x - 5\)?
2. How do you solve \(7 - 3y = 2y + 1\)?
3. If \(5m + 6 = 3m - 4\), what is the value of \(m\)?
4. How can you solve the equation \(-8k + 3 = 4 - 2k\)?
5. What are the steps to solve the equation with parentheses like \(2(3x - 4) = 4x + 8\)?

### Tip

When solving equations, always perform the same operation on both sides to maintain the equality.

Learn how to solve the equation 12 - 6z = 10 - 5z with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear equations. Suitable for students in Grades 7-9.

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