1. **State the problem:** Solve the two-step equation $$65x + 18 = 31$$. 2. **Understand the goal:** We want to isolate $x$ on one side of the equation to find its value. 3. **Step 1 - Subtract 18 from both sides:** $$65x + 18 - 18 = 31 - 18$$ which simplifies to $$65x = 13$$ 4. **Step 2 - Divide both sides by 65 to solve for $x$:** $$\frac{\cancel{65}x}{\cancel{65}} = \frac{13}{65}$$ which simplifies to $$x = \frac{13}{65}$$ 5. **Simplify the fraction:** Both numerator and denominator are divisible by 13: $$x = \frac{\cancel{13} \times 1}{\cancel{13} \times 5} = \frac{1}{5}$$ 6. **Final answer:** $$x = \frac{1}{5}$$ This means the value of $x$ that satisfies the equation is one-fifth.