1. **State the problem:** Solve the linear equation $3x + 5 = 11$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse operations. Remember, whatever you do to one side of the equation, you must do to the other side to keep it balanced. 3. **Step 1:** Subtract 5 from both sides to eliminate the constant term on the left: $$3x + 5 - 5 = 11 - 5$$ which simplifies to $$3x = 6$$ 4. **Step 2:** Divide both sides by 3 to solve for $x$: $$\frac{3x}{3} = \frac{6}{3}$$ which simplifies to $$x = 2$$ 5. **Final answer:** $x = 2$. This means the value of $x$ that satisfies the equation $3x + 5 = 11$ is 2.