1. **State the problem:** Solve the equation $$\sqrt{6w + 5} = \sqrt{2w + 8}$$. 2. **Square both sides** to eliminate the square roots: $$\left(\sqrt{6w + 5}\right)^2 = \left(\sqrt{2w + 8}\right)^2$$ which simplifies to $$6w + 5 = 2w + 8$$. 3. **Isolate the variable** $w$ by subtracting $2w$ from both sides: $$6w - 2w + 5 = 8$$ which simplifies to $$4w + 5 = 8$$. 4. **Subtract 5 from both sides**: $$4w = 8 - 5$$ which is $$4w = 3$$. 5. **Divide both sides by 4**: $$w = \frac{3}{4}$$. 6. **Check for extraneous solutions** by plugging $w = \frac{3}{4}$ back into the original equation: - Left side: $$\sqrt{6 \times \frac{3}{4} + 5} = \sqrt{\frac{18}{4} + 5} = \sqrt{4.5 + 5} = \sqrt{9.5}$$ - Right side: $$\sqrt{2 \times \frac{3}{4} + 8} = \sqrt{\frac{6}{4} + 8} = \sqrt{1.5 + 8} = \sqrt{9.5}$$ Both sides are equal, confirming the solution. **Final answer:** $$w = \frac{3}{4}$$.