1. **State the problem:** Solve the linear equation $9x + 11 = 3$ for $x$. 2. **Isolate the variable term:** Subtract 11 from both sides to get the term with $x$ alone. $$9x + 11 - 11 = 3 - 11$$ $$9x = -8$$ 3. **Solve for $x$:** Divide both sides by 9 to isolate $x$. $$\cancel{9}x = \frac{-8}{\cancel{9}}$$ $$x = -\frac{8}{9}$$ 4. **Final answer:** The solution to the equation is $x = -\frac{8}{9}$. This means that when $x$ is $-\frac{8}{9}$, the original equation $9x + 11 = 3$ holds true.