Solve for \( w \). \[ -\frac{3}{2} w+\frac{1}{4}=-\frac{4}{3} \] Simplify your answer as much as possible.

To solve for \( w \) in the equation \[ -\frac{3}{2} w + \frac{1}{4} = -\frac{4}{3}, \] first, we’ll isolate \( w \). Start by moving \( \frac{1}{4} \) to the right side: \[ -\frac{3}{2} w = -\frac{4}{3} - \frac{1}{4}. \] Next, we need a common denominator to combine the fractions on the right. The least common multiple of 3 and 4 is 12. Thus, we convert the fractions: \[ -\frac{4}{3} = -\frac{16}{12}, \quad \frac{1}{4} = \frac{3}{12}. \] Now substituting back into the equation: \[ -\frac{3}{2} w = -\frac{16}{12} - \frac{3}{12} = -\frac{19}{12}. \] Now, divide both sides by \(-\frac{3}{2}\): \[ w = \frac{-\frac{19}{12}}{-\frac{3}{2}}. \] When dividing fractions, you can multiply by the reciprocal: \[ w = \frac{19}{12} \cdot \frac{2}{3} = \frac{19 \cdot 2}{12 \cdot 3} = \frac{38}{36}. \] Now, simplify \( \frac{38}{36} \): \[ w = \frac{19}{18}. \] Thus, the solution for \( w \) is \[ \boxed{\frac{19}{18}}. \]