Mai solved the equation below incorrectly. Identify Mai's error and then solve the equation correctly. (1)/(3)((1)/(2)x-9)=(1)/(2)(x+18) (1)/(6)x-3=(1)/(2)x+9 (1)/(4)x-3=9 (1)/(4)x=12 x=48

Mai's error occurred in the second step. She incorrectly simplified the equation $\frac{1}{3}(\frac{1}{2}x-9)=\frac{1}{2}(x+18)$ to $\frac{1}{6}x-3=\frac{1}{2}x+9$. The correct simplification should be $\frac{1}{6}x-3=\frac{1}{2}x+9$.<br /><br />Let's solve the equation correctly:<br /><br />$\frac{1}{3}(\frac{1}{2}x-9)=\frac{1}{2}(x+18)$<br /><br />Multiply both sides by 6 to eliminate the fractions:<br /><br />$2(\frac{1}{2}x-9)=3(x+18)$<br /><br />Simplify:<br /><br />$x-18=3x+54$<br /><br />Combine like terms:<br /><br />$-2x=72$<br /><br />Divide both sides by -2:<br /><br />$x=-36$<br /><br />Therefore, the correct solution to the equation is $x=-36$.