1. **State the problem:** Solve the linear equation $3x - 7 = 11$ for $x$. 2. **Add 7 to both sides:** To isolate the term with $x$, add 7 to both sides: $$3x - 7 + 7 = 11 + 7$$ which simplifies to $$3x = 18$$ 3. **Divide both sides by 3:** To solve for $x$, divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{18}{3}$$ which simplifies to $$x = 6$$ 4. **Final answer:** The solution to the equation is $x = 6$. This means when $x$ is 6, the original equation $3x - 7 = 11$ holds true.