1. **State the problem:** Solve the equation $3 + x = 1 + 4x$ for $x$. 2. **Write down the equation:** $$3 + x = 1 + 4x$$ 3. **Isolate the variable $x$:** Subtract $x$ from both sides: $$3 = 1 + 3x$$ 4. **Subtract 1 from both sides:** $$3 - 1 = 3x$$ $$2 = 3x$$ 5. **Divide both sides by 3 to solve for $x$:** $$x = \frac{2}{3}$$ 6. **Final answer:** $$x = \frac{2}{3}$$ This means the value of $x$ that satisfies the equation is $\frac{2}{3}$.