To solve the equation \( 12 = 15\left(z - \dfrac{1}{5}\right) \), we'll follow these steps:

1. **Distribute** the 15 on the right-hand side:
   \[
   12 = 15z - 15 \times \dfrac{1}{5}
   \]

2. **Simplify** the multiplication:
   \[
   12 = 15z - 3
   \]

3. **Add 3** to both sides to isolate the term with \( z \):
   \[
   12 + 3 = 15z
   \]
   \[
   15 = 15z
   \]

4. **Divide** both sides by 15 to solve for \( z \):
   \[
   z = \dfrac{15}{15} = 1
   \]

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

Would you like further details or have any questions?

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Here are some related questions you might find interesting:

1. What happens if you change the constant on the left-hand side?
2. How would the solution change if the equation was \( 12 = 10\left(z - \dfrac{1}{5}\right) \)?
3. Can you solve the equation if the coefficient of \( z \) was different?
4. How does this method apply to solving inequalities?
5. What would the equation look like if you started with \( z = 1 \) and went in reverse?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve the equation 12 = 15(z - 1/5) with a detailed step-by-step solution. This problem involves equations and the distributive property, suitable for students in Grades 7-9.

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