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The equation given is:

\[
\frac{1}{5}(x - 2) = \frac{1}{10}(x + 6)
\]

### Step-by-step solution:

1. **Eliminate the fractions** by multiplying both sides of the equation by the least common denominator (LCD). The LCD of 5 and 10 is 10.

\[
10 \times \frac{1}{5}(x - 2) = 10 \times \frac{1}{10}(x + 6)
\]

This simplifies to:

\[
2(x - 2) = (x + 6)
\]

2. **Distribute** the terms on both sides:

\[
2x - 4 = x + 6
\]

3. **Move all terms involving \(x\)** to one side, and constants to the other:

\[
2x - x = 6 + 4
\]

This simplifies to:

\[
x = 10
\]

Thus, the solution to the equation is:

\[
x = 10
\]

Would you like further clarification or details on any step?

### Here are some related questions:
1. How would you solve the equation if the fractions had different denominators?
2. What happens if both sides of the equation have negative terms?
3. Can this equation be solved using a graphing method?
4. How do you check if your solution to the equation is correct?
5. What would change in the solution if the constants were different (e.g., -2 and 6)?

**Tip**: Always simplify fractions or use the least common denominator to make the equation easier to solve.

Solve the equation \( \frac{1}{5}(x - 2) = \frac{1}{10}(x + 6) \)

Learn how to solve the linear equation \( \frac{1}{5}(x - 2) = \frac{1}{10}(x + 6) \) step-by-step by eliminating fractions and using algebraic methods. This tutorial is suitable for students in Grades 8-10 and covers key algebraic concepts such as the distributive property and solving equations involving fractions.

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