Let's solve the equation step by step:

$6[2 - (2x - 2)] = 2(6 - 3x)$

Step 1: Simplify inside the brackets

First, simplify inside the square brackets on the left-hand side:

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

So, the equation becomes:

$6(4 - 2x) = 2(6 - 3x)$

Step 2: Distribute the 6 and the 2

Distribute the numbers outside the parentheses:

$6 \times (4 - 2x) = 24 - 12x$ $2 \times (6 - 3x) = 12 - 6x$

Now, the equation is:

$24 - 12x = 12 - 6x$

Step 3: Collect like terms

Move all the $x$-terms to one side and the constant terms to the other side. Subtract 12 from both sides:

$24 - 12x - 12 = 12 - 6x - 12$ $12 - 12x = -6x$

Now, add $12x$ to both sides:

$12 = 6x$

Step 4: Solve for $x$

Divide both sides by 6:

$x = 2$

Final Answer:

The solution is $x = 2$.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How would you solve a similar equation with different constants, such as $5[3 - (x - 1)] = 3(5 - 2x)$?
2. Can you explain how distributing works in equations with parentheses?
3. What happens if the variable $x$ is on both sides with a higher degree (like $x^2$)?
4. How would you check if $x = 2$ is the correct solution for this equation?
5. How would the approach differ if there were fractions in the equation?

Tip: Always distribute and simplify each side of the equation before moving terms around!