Let's solve the equation step-by-step:

Given equation:

\[
x - 2(3x - 1) = 7(3 - 2x)
\]

**Step 1: Expand the parentheses**

Distribute the \(-2\) and \(7\) across the terms inside the parentheses:

\[
x - 2 \cdot 3x + 2 \cdot 1 = 7 \cdot 3 - 7 \cdot 2x
\]

This simplifies to:

\[
x - 6x + 2 = 21 - 14x
\]

**Step 2: Combine like terms**

Combine the \(x\) terms on the left side:

\[
-5x + 2 = 21 - 14x
\]

**Step 3: Move all terms involving \(x\) to one side and constants to the other**

Add \(14x\) to both sides:

\[
-5x + 14x + 2 = 21
\]

Simplify:

\[
9x + 2 = 21
\]

Subtract \(2\) from both sides:

\[
9x = 19
\]

**Step 4: Solve for \(x\)**

Divide both sides by \(9\):

\[
x = \frac{19}{9}
\]

**Solution:**

\[
x = \frac{19}{9}
\]

If you need more details or have any questions about the solution, feel free to ask!

### Additional Practice Questions

1. Solve the equation: \(4 - 3(x + 2) = 2(x - 5) - 6\).
2. Simplify the expression: \(5x - 3(2x - 4) + 7\).
3. Solve for \(x\): \(2x - 7 = 3(x + 4) - 2\).
4. Solve the equation: \(\frac{2x + 1}{3} = \frac{x - 2}{5}\).
5. Find the value of \(x\) that satisfies: \(6x - 4(2x - 1) = 3(x + 2)\).

**Tip:** Always perform operations on both sides of the equation to maintain equality.

Learn how to solve the algebraic equation X-2(3x-1)=7(3-2x) with a detailed step-by-step solution. This problem covers key algebraic concepts, including distribution, combining like terms, and solving equations. Suitable for students in Grades 7-9.

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