Let's solve the equation step by step:

The given equation:

$4x - 6 = 3x + 2$

Step 1: Simplify the equation

First, isolate $x$ on one side. Subtract $3x$ from both sides: $4x - 3x - 6 = 2$

This simplifies to: $x - 6 = 2$

Step 2: Solve for $x$

Add 6 to both sides: $x = 2 + 6$

$x = 8$

Final Answer:

$x = 8$

Would you like details or have any further questions? Here are five questions you might explore next:

1. How do we verify that the solution $x = 8$ is correct?
2. What if there were fractions involved in the equation—how would we handle that?
3. Can you show how to graphically represent this equation and its solution?
4. What happens if the equation were $4x - 6 = 3x - 2$ instead?
5. How does solving an inequality differ from solving this equation?

Tip: Always double-check your solution by substituting it back into the original equation to ensure it satisfies the equation!