To solve the equation:

\[
2x - 4 = -x + 3x + 4
\]

### Step 1: Simplify both sides

On the right side of the equation, combine like terms:
\[
2x - 4 = 2x + 4
\]

### Step 2: Isolate the variable

Subtract \(2x\) from both sides to simplify:
\[
-4 = 4
\]

### Step 3: Analyze the result

The statement \(-4 = 4\) is false, indicating there is no value of \(x\) that can satisfy this equation. Therefore, **there is no solution**.

This type of equation is inconsistent and has no solutions.

Would you like a breakdown of these steps? Or do you have any questions?

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Here are some related questions you might find interesting:

1. How can you determine if an equation has no solution or infinitely many solutions?
2. What are some common signs that an equation is inconsistent?
3. How does solving a linear equation differ from solving a quadratic one?
4. Can systems of equations also have no solutions? Why or why not?
5. What does it mean graphically when an equation has no solution?

**Tip:** If an equation simplifies to a false statement (like \(-4 = 4\)), it has no solutions.

Understand why the equation 2x - 4 = -x + 3x + 4 has no solution by simplifying and analyzing steps. This problem introduces concepts in algebra, focusing on linear and inconsistent equations. Ideal for students in Grades 7-9.

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