1. **State the problem:** Solve the equation $19 - 4x = 2x + 1$ for $x$. 2. **Write down the equation:** $$19 - 4x = 2x + 1$$ 3. **Goal:** Isolate $x$ on one side of the equation. 4. **Add $4x$ to both sides to move all $x$ terms to the right:** $$19 = 2x + 1 + 4x$$ 5. **Simplify the right side:** $$19 = 6x + 1$$ 6. **Subtract 1 from both sides to isolate the term with $x$:** $$19 - 1 = 6x$$ $$18 = 6x$$ 7. **Divide both sides by 6 to solve for $x$:** $$x = \frac{18}{6}$$ $$x = 3$$ **Final answer:** $x = 3$