Solve the following equation. \[ \frac{-3}{5} x+\frac{1}{6}=\frac{-1}{3} x-\frac{2}{3} \]

Solve the equation \( \frac{-3}{5}x+\frac{1}{6}=\frac{-1}{3}x-\frac{2}{3} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{-3}{5}x+\frac{1}{6}=\frac{-1}{3}x-\frac{2}{3}\) - step1: Rewrite the fraction: \(-\frac{3}{5}x+\frac{1}{6}=-\frac{1}{3}x-\frac{2}{3}\) - step2: Multiply both sides of the equation by LCM: \(\left(-\frac{3}{5}x+\frac{1}{6}\right)\times 30=\left(-\frac{1}{3}x-\frac{2}{3}\right)\times 30\) - step3: Calculate: \(-18x+5=\left(-\frac{1}{3}x-\frac{2}{3}\right)\times 30\) - step4: Calculate: \(-18x+5=-10x-20\) - step5: Move the expression to the left side: \(-18x+10x=-20-5\) - step6: Add and subtract: \(-8x=-20-5\) - step7: Add and subtract: \(-8x=-25\) - step8: Change the signs: \(8x=25\) - step9: Divide both sides: \(\frac{8x}{8}=\frac{25}{8}\) - step10: Divide the numbers: \(x=\frac{25}{8}\) The solution to the equation \(\frac{-3}{5}x+\frac{1}{6}=\frac{-1}{3}x-\frac{2}{3}\) is \(x=\frac{25}{8}\) or \(x=3.125\).