To solve the equation \( 3(4x - 7) = 11x - 19 \), follow these steps:

1. **Expand the left side**:
   \[
   3(4x - 7) = 12x - 21
   \]
   So the equation becomes:
   \[
   12x - 21 = 11x - 19
   \]

2. **Move the variable terms to one side**:
   Subtract \( 11x \) from both sides:
   \[
   12x - 11x - 21 = -19
   \]
   Simplifying:
   \[
   x - 21 = -19
   \]

3. **Solve for \( x \)**:
   Add 21 to both sides:
   \[
   x = -19 + 21
   \]
   \[
   x = 2
   \]

Thus, the solution is \( x = 2 \).

Would you like further clarification or details on this process? 

Here are some related questions you might explore:
1. What happens if both sides of the equation are multiplied by a constant?
2. Can you solve \( 2(5x + 3) = 9x - 7 \)?
3. How do you solve an equation with variables on both sides?
4. What would happen if the equation had no solution?
5. How can you check if your solution is correct?

**Tip**: Always verify your solution by substituting it back into the original equation to see if both sides are equal.

Learn how to solve the linear equation 3(4x-7)=11x-19 with a detailed step-by-step solution. This problem covers key algebraic concepts such as the distributive property and solving equations with variables on both sides. Suitable for students in Grades 8-10.

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