Solve for \( r \). Give an exact answer. \( \frac{1}{2} r-3=3\left(4-\frac{3}{2} r\right) \)

Solve the equation \( \frac{1}{2}r-3=3\left(4-\frac{3}{2}r\right) \). Solve the equation by following steps: - step0: Solve for \(r\): \(\frac{1}{2}r-3=3\left(4-\frac{3}{2}r\right)\) - step1: Expand the expression: \(\frac{1}{2}r-3=12-\frac{9}{2}r\) - step2: Multiply both sides of the equation by LCM: \(\left(\frac{1}{2}r-3\right)\times 2=\left(12-\frac{9}{2}r\right)\times 2\) - step3: Calculate: \(r-6=\left(12-\frac{9}{2}r\right)\times 2\) - step4: Calculate: \(r-6=24-9r\) - step5: Move the expression to the left side: \(r+9r=24+6\) - step6: Add and subtract: \(10r=24+6\) - step7: Add and subtract: \(10r=30\) - step8: Divide both sides: \(\frac{10r}{10}=\frac{30}{10}\) - step9: Divide the numbers: \(r=3\) The solution to the equation \( \frac{1}{2}r-3=3\left(4-\frac{3}{2}r\right) \) is \( r=3 \).