1. **State the problem:** Solve the linear equation $3x = 4x + 1$ for $x$. 2. **Recall the rule:** To solve for $x$, we want to isolate $x$ on one side of the equation. 3. **Subtract $4x$ from both sides:** $$3x - 4x = 4x + 1 - 4x$$ which simplifies to $$-x = 1$$ 4. **Multiply both sides by $-1$ to solve for $x$:** $$x = -1$$ 5. **Final answer:** $$x = -1$$ This means the value of $x$ that satisfies the equation is $-1$.