1. The problem is to solve the equation $$3x - 7 = 11$$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We add 7 to both sides to cancel the $-7$. 3. Adding 7 to both sides: $$3x - 7 + 7 = 11 + 7$$ which simplifies to $$3x = 18$$ 4. Next, divide both sides by 3 to solve for $x$: $$\frac{3x}{3} = \frac{18}{3}$$ which can be shown as $$\frac{\cancel{3}x}{\cancel{3}} = \frac{18}{3}$$ 5. Simplifying the division: $$x = 6$$ 6. Therefore, the solution to the equation is $x = 6$. This means when $x$ is 6, the original equation holds true.