Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1

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Start by isolating the radical expression on one side of the equation, which is already done: $\sqrt{6x + 1} = x - 1$.

To eliminate the square root, square both sides of the equation: $\left(\sqrt{6x + 1}\right)^2 = (x - 1)^2$.

Simplify both sides: $6x + 1 = (x - 1)^2$.

Expand the right side using the formula $(a - b)^2 = a^2 - 2ab + b^2$: $6x + 1 = x^2 - 2x + 1$.

Rearrange the equation to set it equal to zero by moving all terms to one side: $0 = x^2 - 2x + 1 - 6x - 1$, then simplify the right side.

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