To solve the equation 2(x - 4) - 2x = 2x - 10, let's go through the steps in order:
Step 1: Distribute the 2 to the terms in the parentheses
2 * x = 2x
2 * -4 = -8
So, the equation becomes 2x - 8 - 2x = 2x - 10
Step 2: Combine like terms on both sides of the equation
On the left side, 2x - 2x cancels out, leaving -8.
On the right side, we have 2x - 10.
So, the equation now becomes -8 = 2x - 10.
Step 3: Bring all x terms to one side by subtracting 2x from both sides of the equation
-8 - 2x = 2x - 10 - 2x
This simplifies to -8 - 2x = -10.
Step 4: Now, let's isolate the x term by adding 8 to both sides of the equation
-8 + 8 - 2x = -10 + 8
This simplifies to -2x = -2.
Step 5: Finally, solve for x by dividing both sides of the equation by -2
-2x / -2 = -2 / -2
This simplifies to x = 1.
Therefore, the solution for the equation 2(x - 4) - 2x = 2x - 10 is x = 1.