1. **State the problem:** Solve the two-step equation $$3x + 1 = 7$$. 2. **Identify the goal:** We want to isolate the variable $x$ on one side of the equation. 3. **Use inverse operations:** Start by undoing the addition of 1 by subtracting 1 from both sides: $$3x + 1 - 1 = 7 - 1$$ which simplifies to $$3x = 6$$ 4. **Eliminate the coefficient:** To isolate $x$, divide both sides by 3: $$\frac{3x}{\cancel{3}} = \frac{6}{\cancel{3}}$$ which simplifies to $$x = 2$$ 5. **Check the solution:** Substitute $x = 2$ back into the original equation: $$3(2) + 1 = 6 + 1 = 7$$ Since both sides equal 7, the solution is correct. **Final answer:** $$x = 2$$