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!