Let's solve the equation step by step:

### Given equation:
\[
5x - 2(2x - 1) = 6
\]

1. **Distribute the -2 across the parentheses:**
\[
5x - 2 \cdot 2x + 2 \cdot 1 = 6
\]
This simplifies to:
\[
5x - 4x + 2 = 6
\]

2. **Combine like terms:**
\[
(5x - 4x) + 2 = 6
\]
\[
x + 2 = 6
\]

3. **Isolate \(x\) by subtracting 2 from both sides:**
\[
x = 6 - 2
\]
\[
x = 4
\]

### Final solution:
\[
x = 4
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What would the solution be if the constant on the right side was different, such as 10?
2. How would you solve the equation if the terms were rearranged as \(5x = 6 + 2(2x - 1)\)?
3. Can you verify the solution by substituting \(x = 4\) back into the original equation?
4. How does distributing negative values across parentheses change the equation-solving process?
5. What happens if you divide the whole equation by 2 before distributing?

**Tip:** Always remember to combine like terms before isolating the variable—it simplifies your work!

Learn how to solve the linear equation 5x - 2(2x-1) = 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, such as applying the distributive property and combining like terms. Ideal for students in Grades 6-8 looking to strengthen their equation-solving skills.

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