To solve the inequality \(3x - 4 > 6 + 5x\), follow these steps:

### Step 1: Get all terms with \(x\) on one side.
Subtract \(5x\) from both sides:
\[
3x - 5x - 4 > 6
\]
This simplifies to:
\[
-2x - 4 > 6
\]

### Step 2: Isolate the \(x\)-term.
Add 4 to both sides:
\[
-2x > 10
\]

### Step 3: Solve for \(x\).
Divide both sides by \(-2\). Remember, dividing by a negative number flips the inequality:
\[
x < -5
\]

### Final Answer:
The solution is \(x < -5\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve inequalities with fractions?
2. What happens when you multiply or divide an inequality by a negative number?
3. How do you graph the solution of \(x < -5\) on a number line?
4. Can you solve \(2x + 7 \leq 3x - 5\)?
5. How do you solve a system of inequalities?

**Tip:** Always remember that dividing or multiplying by a negative number reverses the inequality sign.

Learn how to solve the inequality 3x - 4 > 6 + 5x with step-by-step guidance. This algebra problem demonstrates how to isolate variables and handle inequality reversals. Suitable for students in Grades 7-9.

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