Let's solve the equation step by step:

Given equation:
\[
-2(1 - 5x) = -102
\]

1. **Distribute the \(-2\) on the left side:**

   \[
   -2 \cdot 1 + (-2) \cdot (-5x) = -102
   \]

   Simplifying:
   \[
   -2 + 10x = -102
   \]

2. **Move the constant term to the right side:**

   Add 2 to both sides:
   \[
   10x = -102 + 2
   \]
   Simplifying:
   \[
   10x = -100
   \]

3. **Isolate the variable:**

   Divide both sides by 10:
   \[
   x = \frac{-100}{10}
   \]
   Simplifying:
   \[
   x = -10
   \]

So, the solution is \( x = -10 \).

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

Here are 5 related questions to further explore this topic:
1. What happens if the equation is \(2(1 - 5x) = 102\)?
2. How do you solve an equation with multiple distributions, like \(3(2x - 4) - 5(x + 6) = 20\)?
3. What if the equation had a fraction, such as \(-\frac{1}{2}(1 - 5x) = -51\)?
4. How can you verify the solution of an equation?
5. How do you solve equations involving absolute values, like \(|2x - 3| = 7\)?

**Tip:** Always perform distribution carefully and check your work by substituting the solution back into the original equation.

Learn how to solve the equation -2(1 - 5x) = -102 with a detailed step-by-step solution. This problem involves distributing, moving constants, and isolating variables. Suitable for students in Grades 7-9.

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