To solve the equation \(5(2z - 9) = -35\), follow these steps:

1. **Distribute the 5** across the terms inside the parentheses:
   \[
   5 \cdot 2z + 5 \cdot (-9) = 10z - 45
   \]
   So, the equation becomes:
   \[
   10z - 45 = -35
   \]

2. **Add 45** to both sides to isolate the term with \(z\):
   \[
   10z - 45 + 45 = -35 + 45
   \]
   Simplifying this, you get:
   \[
   10z = 10
   \]

3. **Divide by 10** on both sides to solve for \(z\):
   \[
   z = \frac{10}{10}
   \]
   Simplifying, you get:
   \[
   z = 1
   \]

So, the solution is \(z = 1\).

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

Here are 5 related questions:
1. What is the solution to \(4(3z - 7) = -20\)?
2. How do you solve the equation \(6(2z - 5) = -24\)?
3. What happens if you change the equation to \(5(2z - 9) = -25\)?
4. How do you solve for \(z\) in the equation \(7(3z + 4) = 21\)?
5. What is the effect of adding a constant on both sides, like in \(5(2z - 9) + 10 = -25\)?

**Tip:** When solving equations, always double-check your distribution to ensure no mistakes were made when multiplying each term.

Learn how to solve the equation 5(2z - 9) = -35 with a detailed step-by-step solution. This problem involves algebraic equations and the distributive property, suitable for Grades 7-9 students.

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