1. **State the problem:** Solve the equation $$\sqrt{5x - 1} + 4 = 11$$ for $x$. 2. **Isolate the square root term:** Subtract 4 from both sides to get $$\sqrt{5x - 1} = 11 - 4$$ 3. Simplify the right side: $$\sqrt{5x - 1} = 7$$ 4. **Square both sides** to eliminate the square root: $$\left(\sqrt{5x - 1}\right)^2 = 7^2$$ $$5x - 1 = 49$$ 5. **Solve for $x$:** Add 1 to both sides: $$5x = 49 + 1$$ $$5x = 50$$ 6. Divide both sides by 5: $$x = \frac{50}{5}$$ $$x = 10$$ 7. **Check the solution:** Substitute $x=10$ back into the original equation: $$\sqrt{5(10) - 1} + 4 = \sqrt{50 - 1} + 4 = \sqrt{49} + 4 = 7 + 4 = 11$$ The left side equals the right side, so $x=10$ is the correct solution.