To solve the equation \( 7(z - 10) = -7 \), follow these steps:

1. Distribute the 7 on the left-hand side:
   \[
   7z - 70 = -7
   \]

2. Add 70 to both sides to isolate the term with \( z \):
   \[
   7z = -7 + 70
   \]
   \[
   7z = 63
   \]

3. Divide both sides by 7:
   \[
   z = \frac{63}{7}
   \]
   \[
   z = 9
   \]

So, the solution is \( z = 9 \).

Would you like more details on any step?

Here are 5 related questions to explore:

1. How would the solution change if the equation were \( 7(z - 10) = 7 \)?
2. What happens if we replace the 7 with another constant in the equation \( 7(z - 10) = -7 \)?
3. How can we solve a similar equation involving fractions, like \( \frac{1}{2}(z - 10) = -7 \)?
4. How can we verify that our solution for \( z \) is correct?
5. What is the general process for solving linear equations with one variable?

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

Learn how to solve the linear equation 7(z - 10) = -7 with a step-by-step solution. This problem demonstrates the use of the distributive property and the properties of equality, making it suitable for students in Grades 6-8.

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