Let's solve the equation step by step:

Given equation: $2x - 6x - 1 = 5 - 2x$

Step 1: Combine like terms on the left side

$(2x - 6x) - 1 = -4x - 1$ So, the equation simplifies to: $-4x - 1 = 5 - 2x$

Step 2: Add $2x$ to both sides to move the $x$ terms to one side:

$-4x + 2x - 1 = 5 - 2x + 2x$ This simplifies to: $-2x - 1 = 5$

Step 3: Add 1 to both sides to isolate the term with $x$:

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

Step 4: Divide both sides by $-2$ to solve for $x$:

$x = \frac{6}{-2} = -3$

So, the solution is: $\boxed{-3}$

Would you like more details on any of these steps or have any questions?

Here are 5 related questions:

1. How would the solution change if the constant on the right side were different?
2. Can you verify the solution by substituting $x = -3$ back into the original equation?
3. What if the equation had a squared term, such as $2x^2 - 6x - 1 = 5 - 2x$?
4. How do the steps differ if the equation had fractions?
5. How would you solve the equation if the $x$ terms were on both sides but with different coefficients?

Tip: Always check your solution by substituting it back into the original equation. This helps to confirm that your answer is correct.