Solve the given equation for \( d \) \( \frac{3}{4}(2 d-3)=3(d+2)-\frac{1}{4} d \)

To solve the equation \( \frac{3}{4}(2 d-3)=3(d+2)-\frac{1}{4} d \), let's start by simplifying both sides. 1. Distributing \( \frac{3}{4} \) on the left side: \[ \frac{3}{4} \cdot 2d - \frac{3}{4} \cdot 3 = \frac{3}{2}d - \frac{9}{4} \] 2. Expanding the right side: \[ 3(d + 2) - \frac{1}{4}d = 3d + 6 - \frac{1}{4}d \] To combine the \( d \) terms: \[ 3d - \frac{1}{4}d = \frac{12}{4}d - \frac{1}{4}d = \frac{11}{4}d \] So the right side becomes: \[ \frac{11}{4}d + 6 \] Now we can set the simplified expressions equal to each other: \[ \frac{3}{2}d - \frac{9}{4} = \frac{11}{4}d + 6 \] 3. To eliminate the fractions, multiply everything by 4: \[ 4 \cdot \frac{3}{2}d - 4 \cdot \frac{9}{4} = 4 \cdot \frac{11}{4}d + 4 \cdot 6 \] This simplifies to: \[ 6d - 9 = 11d + 24 \] 4. Move all terms involving \( d \) to one side and constants to the other side: \[ 6d - 11d = 24 + 9 \] This simplifies to: \[ -5d = 33 \] 5. Finally, divide by -5: \[ d = -\frac{33}{5} \] Thus, the solution for \( d \) is: \[ d = -6.6 \]