1. **State the problem:** Solve the equation $$-2\sqrt{24x} + 13 = -11$$ for $x$. 2. **Isolate the square root term:** Subtract 13 from both sides: $$-2\sqrt{24x} = -11 - 13$$ $$-2\sqrt{24x} = -24$$ 3. **Divide both sides by -2:** $$\cancel{-2}\sqrt{24x} = \frac{-24}{\cancel{-2}}$$ $$\sqrt{24x} = 12$$ 4. **Square both sides to eliminate the square root:** $$\left(\sqrt{24x}\right)^2 = 12^2$$ $$24x = 144$$ 5. **Solve for $x$ by dividing both sides by 24:** $$x = \frac{144}{24}$$ $$x = 6$$ 6. **Check the solution:** Substitute $x=6$ back into the original equation: $$-2\sqrt{24 \times 6} + 13 = -2\sqrt{144} + 13 = -2 \times 12 + 13 = -24 + 13 = -11$$ The left side equals the right side, so $x=6$ is the correct solution. **Final answer:** $$x = 6$$