To solve the equation \(3x - 4 = -x + 6 + 11x + 4x - 3\), follow these steps:

1. **Simplify both sides of the equation:**

   On the right-hand side, combine like terms:
   \[
   -x + 11x + 4x = 14x
   \]
   Then, combine the constants \(6 - 3 = 3\).

   So the equation simplifies to:
   \[
   3x - 4 = 14x + 3
   \]

2. **Move the variable terms to one side:**

   Subtract \(14x\) from both sides to get all the \(x\) terms on one side:
   \[
   3x - 14x - 4 = 3
   \]
   Simplify:
   \[
   -11x - 4 = 3
   \]

3. **Move the constant terms to the other side:**

   Add 4 to both sides to isolate the term with \(x\):
   \[
   -11x = 3 + 4
   \]
   Simplify:
   \[
   -11x = 7
   \]

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

   Divide both sides by \(-11\):
   \[
   x = \frac{7}{-11}
   \]
   Simplify:
   \[
   x = -\frac{7}{11}
   \]

So, the solution is \(x = -\frac{7}{11}\).

Would you like any details or have any questions?

Here are five related questions you might find useful:

1. How do you solve equations with multiple terms on one side?
2. What strategies can you use to simplify complex linear equations?
3. How do you solve equations involving decimals or fractions?
4. What is the significance of checking your solution by substituting it back into the original equation?
5. How do you approach solving equations with distributive properties?

**Tip:** Always combine like terms before moving variables to one side—it simplifies the equation and reduces errors!

Learn how to solve the equation 3x - 4 = -x + 6 + 11x + 4x - 3 step-by-step with detailed instructions. This problem involves combining like terms and simplifying a linear equation. Suitable for students in Grades 7-9.

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