\( \sqrt{7 x-6}=1 \) The solution set is \( \square \cdot \square[\square] \)

Solve the equation \( \sqrt{7x-6}=1 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\sqrt{7x-6}=1\) - step1: Find the domain: \(\sqrt{7x-6}=1,x\geq \frac{6}{7}\) - step2: Raise both sides to the \(2\)-th power\(:\) \(\left(\sqrt{7x-6}\right)^{2}=1^{2}\) - step3: Evaluate the power: \(7x-6=1\) - step4: Move the constant to the right side: \(7x=1+6\) - step5: Add the numbers: \(7x=7\) - step6: Divide both sides: \(\frac{7x}{7}=\frac{7}{7}\) - step7: Divide the numbers: \(x=1\) - step8: Check if the solution is in the defined range: \(x=1,x\geq \frac{6}{7}\) - step9: Find the intersection: \(x=1\) - step10: Check the solution: \(x=1\) The solution to the equation \( \sqrt{7x-6}=1 \) is \( x=1 \). Therefore, the solution set is \( \boxed{1} \).