To solve the equation 5x - 2(2x - 7) = 2(3x - 1), we will follow the steps below:

1. Distribute the values inside the brackets:
5x - 4x + 14 = 6x - 2

2. Combine like terms on both sides of the equation:
x + 14 = 6x - 2

3. Move all the terms containing x to one side of the equation by adding or subtracting:
x - 6x = -2 - 14

4. Simplify:
-5x = -16

5. Divide both sides of the equation by -5 to solve for x:
x = (-16) / (-5)

6. Perform the division:
x = 16/5

Therefore, the solution to the equation 5x - 2(2x - 7) = 2(3x - 1) is x = 16/5 or 3.2.

Explanation of Steps:

1. Distributing the values inside the brackets is done using the distributive property of multiplication over addition/subtraction. In this case, we multiply -2 by both terms inside the first bracket and 2 by both terms inside the second bracket.

2. Combining like terms involves adding or subtracting terms that have the same variable and exponent. In this case, we combine the x terms on the left side of the equation and the constant terms on the right side.

3. Moving terms involves isolating the variable by adding or subtracting terms on both sides of the equation. In this case, we move the 6x term to the right side of the equation by subtracting x from both sides.

4. Simplifying involves performing arithmetic operations to simplify the equation. In this case, we subtract 2 from -14 to get -16.

5. Dividing both sides of the equation by -5 is done to solve for x. Dividing by -5 allows us to isolate x on one side of the equation.

6. Performing the division simplifies the equation further. In this case, -16 divided by -5 gives us 16/5 or 3.2.

Therefore, the solution to the equation is x = 16/5 or 3.2.