6. Milo solved the following inequality. Complete the statement to describe the solution set for the Inequality. \[ 6(1-2 x)>6-6 x \] The solution set has \[ 6-12 x>6-\frac{6 x}{+6 x} \] Select - one solution. - no solution. - infinite solutions. \( 6-6 x>6 \) 6 \( \frac{-6 x}{-6}>\frac{0}{-6} \) \( -\infty, 1) \)

Solve the equation \( 6-12x>6-\frac{6x}{+6x} \). Solve the inequality by following steps: - step0: Solve for \(x\): \(6-12x>6-\frac{6x}{6x}\) - step1: Find the domain: \(6-12x>6-\frac{6x}{6x},x\neq 0\) - step2: Cancel equal terms: \(-12x>-\frac{6x}{6x}\) - step3: Divide the terms: \(-12x>-1\) - step4: Change the signs: \(12x<1\) - step5: Divide both sides: \(\frac{12x}{12}<\frac{1}{12}\) - step6: Divide the numbers: \(x<\frac{1}{12}\) - step7: Check if the solution is in the defined range: \(x<\frac{1}{12},x\neq 0\) - step8: Find the intersection: \(x \in \left(-\infty,0\right)\cup \left(0,\frac{1}{12}\right)\) The solution set for the inequality \(6(1-2x)>6-6x\) is \(x \in (-\infty,0) \cup (0,\frac{1}{12})\). Therefore, the solution set has infinite solutions.