1. **State the problem:** Solve the equation $-2\sqrt{2}r + 5 = 6$ for $r$. 2. **Isolate the term with $r$:** Subtract 5 from both sides: $$-2\sqrt{2}r + 5 - 5 = 6 - 5$$ $$-2\sqrt{2}r = 1$$ 3. **Divide both sides by $-2\sqrt{2}$ to solve for $r$:** $$r = \frac{1}{-2\sqrt{2}}$$ 4. **Simplify the fraction:** $$r = -\frac{1}{2\sqrt{2}}$$ 5. **Rationalize the denominator:** Multiply numerator and denominator by $\sqrt{2}$: $$r = -\frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2 \times 2} = -\frac{\sqrt{2}}{4}$$ **Final answer:** $$r = -\frac{\sqrt{2}}{4}$$