1. **State the problem:** Solve for $x$ in the equation $$1 = \sqrt{2x - 6} - 1.$$ 2. **Isolate the square root:** Add 1 to both sides to get $$1 + 1 = \sqrt{2x - 6}$$ which simplifies to $$2 = \sqrt{2x - 6}.$$ 3. **Square both sides:** To eliminate the square root, square both sides: $$2^2 = (\sqrt{2x - 6})^2$$ which gives $$4 = 2x - 6.$$ 4. **Solve for $x$:** Add 6 to both sides: $$4 + 6 = 2x$$ so $$10 = 2x.$$ Divide both sides by 2: $$x = \frac{10}{2} = 5.$$ 5. **Check for extraneous solutions:** Substitute $x=5$ back into the original equation: $$\sqrt{2(5) - 6} - 1 = \sqrt{10 - 6} - 1 = \sqrt{4} - 1 = 2 - 1 = 1,$$ which matches the right side. So $x=5$ is a valid solution. **Final answer:** $$x = 5.$$