Let's solve the equation step by step:

The equation is:

\[
3(1 - (1 - 2(1 - x))) = 4 - 2x
\]

### Step 1: Simplify inside the parentheses
First, simplify the innermost parentheses:

\[
1 - x
\]

Multiply by 2:

\[
2(1 - x) = 2 - 2x
\]

Now, substitute back into the equation:

\[
3(1 - (1 - (2 - 2x))) = 4 - 2x
\]

### Step 2: Simplify further
Simplify inside the parentheses:

\[
1 - (1 - (2 - 2x)) = 1 - (1 - 2 + 2x) = 1 - (-1 + 2x) = 1 + 1 - 2x = 2 - 2x
\]

Now substitute back into the equation:

\[
3(2 - 2x) = 4 - 2x
\]

### Step 3: Distribute the 3
Distribute the 3 on the left side:

\[
6 - 6x = 4 - 2x
\]

### Step 4: Combine like terms
Move all the \(x\) terms to one side and the constants to the other side:

\[
-6x + 2x = 4 - 6
\]

Simplify:

\[
-4x = -2
\]

### Step 5: Solve for \(x\)
Divide both sides by \(-4\):

\[
x = \frac{-2}{-4} = \frac{1}{2}
\]

### Final Answer:

\[
x = \frac{1}{2}
\]

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

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Here are some related questions you might find interesting:
1. How do you solve equations with nested parentheses?
2. What is the process for distributing multiplication over subtraction?
3. How do you simplify equations with multiple variables?
4. How can you check if your solution to an equation is correct?
5. What are the common mistakes to avoid when solving linear equations?

**Tip:** Always simplify inside the parentheses first when solving equations with nested operations.

Learn how to solve the equation 3(1-(1-2(1-x)))=4-2x with detailed step-by-step solutions. This problem involves simplifying equations with nested parentheses and applying the distributive property. Suitable for students in Grades 9-12.

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