1. **State the problem:** Solve the linear equation $4x + 6 = 6x$ for $x$. 2. **Recall the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equation. We can do this by moving all terms involving $x$ to one side and constants to the other. 3. **Step-by-step solution:** - Start with the equation: $$4x + 6 = 6x$$ - Subtract $4x$ from both sides to get all $x$ terms on the right: $$6 = 6x - 4x$$ - Simplify the right side: $$6 = 2x$$ - Divide both sides by 2 to isolate $x$: $$x = \frac{6}{2}$$ - Simplify the fraction: $$x = 3$$ 4. **Answer:** The solution to the equation $4x + 6 = 6x$ is $x = 3$. This means when $x$ is 3, both sides of the equation are equal.