1. **State the problem:** Solve the equation $15x - 10 = 65$ for $x$. 2. **Add 10 to both sides:** $$15x - 10 + 10 = 65 + 10$$ $$15x = 75$$ 3. **Express 15 as a product:** $$15x = 3 \cdot 5 \cdot x$$ 4. **Divide both sides by 15 to isolate $x$:** $$\frac{\cancel{15}x}{\cancel{15}} = \frac{75}{15}$$ $$x = 5$$ 5. **Final answer:** $$x = 5$$ This means the value of $x$ that satisfies the equation is 5.