To solve the equation \( 10(z - 10) = -40 \), follow these steps:

### Step 1: Distribute the 10 on the left side.
\[
10(z - 10) = 10z - 100
\]
So the equation becomes:
\[
10z - 100 = -40
\]

### Step 2: Add 100 to both sides to isolate the term with \( z \).
\[
10z - 100 + 100 = -40 + 100
\]
This simplifies to:
\[
10z = 60
\]

### Step 3: Divide both sides by 10 to solve for \( z \).
\[
z = \frac{60}{10}
\]
\[
z = 6
\]

Thus, the solution is \( z = 6 \).

Would you like a deeper explanation or have any questions?

Here are 5 related questions to consider:
1. How would the solution change if the equation were \( 5(z - 10) = -40 \)?
2. What is the general process for solving equations with distribution?
3. How can you check if your solution is correct?
4. How does isolating the variable work in multi-step equations?
5. What if there were a fraction instead of 10 in the equation?

**Tip:** Always simplify both sides of the equation step by step to avoid mistakes!

Explore how to solve the linear equation 10(z - 10) = -40 using step-by-step algebraic techniques. This problem demonstrates the distributive property and methods for isolating variables. Ideal for students in Grades 6-8.

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