1. **State the problem:** Solve the equation $x - 5.7 = 19$ for $x$. 2. **Formula and rules:** To isolate $x$, add $5.7$ to both sides of the equation. This uses the addition property of equality which states that adding the same number to both sides keeps the equation balanced. 3. **Intermediate work:** $$x - 5.7 + 5.7 = 19 + 5.7$$ $$x + \cancel{-5.7} + \cancel{5.7} = 19 + 5.7$$ $$x = 24.7$$ 4. **Explanation:** By adding $5.7$ to both sides, the $-5.7$ on the left cancels out, leaving $x$ alone. On the right side, $19 + 5.7$ equals $24.7$. 5. **Final answer:** $$x = 24.7$$