Let's solve the equation step by step:

Given:
\[
4(X - 3) - 7(X - 4) = 6 - X
\]

### Step 1: Distribute the constants in the parentheses.
\[
4 \cdot (X) - 4 \cdot (3) - 7 \cdot (X) + 7 \cdot (4) = 6 - X
\]
Simplifying:
\[
4X - 12 - 7X + 28 = 6 - X
\]

### Step 2: Combine like terms on the left side.
\[
(4X - 7X) + (-12 + 28) = 6 - X
\]
\[
-3X + 16 = 6 - X
\]

### Step 3: Move the variable terms to one side of the equation.
Add \(3X\) to both sides:
\[
16 = 6 + 2X
\]

### Step 4: Isolate \(X\).
Subtract 6 from both sides:
\[
10 = 2X
\]
Divide both sides by 2:
\[
X = 5
\]

So, the solution is \(X = 5\).

Would you like any further details or explanations on this solution?

Here are 5 related questions to practice:

1. Solve for \(X\): \(3(X + 2) - 4(X - 1) = 7\).
2. Simplify and solve: \(2(2X - 3) = 3X + 7\).
3. Solve the equation: \(5(X - 1) + 2(2X + 3) = 4X + 10\).
4. Find \(X\) in the equation: \(8(X + 1) - 5(X - 2) = 12\).
5. Solve for \(X\): \(7(X - 4) - 2(X + 3) = X + 5\).

**Tip:** Always combine like terms and isolate the variable on one side to solve linear equations efficiently.

Learn how to solve the linear equation 4(X-3)-7(X-4)=6-X step-by-step with detailed explanations. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 7-9.

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