1. The problem is to solve the equation $3x + 1 = 7$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, we need to undo the operations around it. Here, $x$ is multiplied by 3 and then 1 is added. 3. First, subtract 1 from both sides to remove the constant term on the left: $$3x + 1 - 1 = 7 - 1$$ which simplifies to $$3x = 6$$ 4. Next, divide both sides by 3 to solve for $x$: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{6}{3}$$ which simplifies to $$x = 2$$ 5. Check the solution by substituting $x=2$ back into the original equation: $$3(2) + 1 = 6 + 1 = 7$$ which is true. Therefore, the solution is $x = 2$.