To solve the equation 5(9z + 2) - 5 = 815z, we will first simplify the left side of the equation by applying the distributive property. Then, we will combine like terms and isolate the variable z.
Let's go step by step:
1. Distribute the 5 across the parentheses: 5 * 9z + 5 * 2 - 5 = 815z
This simplifies to: 45z + 10 - 5 = 815z
2. Combine like terms on the left side: 45z + 5 = 815z
3. Now, let's isolate z. Move the term with z to one side and the constant term to the other side. We can do this by subtracting 45z from both sides: 45z - 45z + 5 = 815z - 45z
This simplifies to: 5 = 770z
4. Finally, solve for z by dividing both sides of the equation by 770: 5/770 = z
This simplifies to: z = 1/154
So, the solution to the equation 5(9z + 2) - 5 = 815z is z = 1/154.