To solve for $x$ in the equation:

$5x - 2(2x - 1) = 6$

we'll first distribute the $-2$ through the parentheses.

Step 1: Distribute the $-2$

$5x - 2 \cdot 2x + 2 \cdot 1 = 6$

This simplifies to:

$5x - 4x + 2 = 6$

Step 2: Combine like terms

Combine the terms involving $x$:

$(5x - 4x) + 2 = 6$

which simplifies to:

$x + 2 = 6$

Step 3: Solve for $x$

Subtract 2 from both sides:

$x = 6 - 2$

$x = 4$

Final Answer:

$x = 4$

Would you like further details or have any questions about the solution?

---

Here are some related questions you might find interesting:

1. What if there was a different coefficient in front of $x$?
2. How would the solution change if the constant on the right side were different?
3. What happens if both sides of the equation have expressions with $x$?
4. How can we check if our solution for $x$ is correct?
5. What are some methods for solving more complex algebraic equations?

Tip: Always double-check your distribution and combining of like terms to avoid simple mistakes in algebra.