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!

Discover how to solve the linear equation 6[2 − (2x − 2)] = 2(6 − 3x) with a step-by-step guide. This problem involves algebraic concepts such as the distributive property and solving for variables, making it perfect for students in Grades 8-10.

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