1. **State the problem:** Solve the matrix equation $$2X + A = B$$ for matrix $$X$$, where $$A = \begin{bmatrix}0 & -9 \\ 2 & 6 \\ -3 & 5\end{bmatrix}$$ and $$B = \begin{bmatrix}2 & -3 \\ 4 & -7 \\ 7 & 5\end{bmatrix}$$. 2. **Formula and rules:** To isolate $$X$$, subtract $$A$$ from both sides: $$2X + A - A = B - A \implies 2X = B - A$$ Then divide both sides by 2 (scalar division of each element): $$X = \frac{B - A}{2}$$ 3. **Calculate $$B - A$$:** $$B - A = \begin{bmatrix}2 - 0 & -3 - (-9) \\ 4 - 2 & -7 - 6 \\ 7 - (-3) & 5 - 5\end{bmatrix} = \begin{bmatrix}2 & 6 \\ 2 & -13 \\ 10 & 0\end{bmatrix}$$ 4. **Divide by 2:** $$X = \frac{1}{2} \times \begin{bmatrix}2 & 6 \\ 2 & -13 \\ 10 & 0\end{bmatrix} = \begin{bmatrix}\frac{2}{2} & \frac{6}{2} \\ \frac{2}{2} & \frac{-13}{2} \\ \frac{10}{2} & \frac{0}{2}\end{bmatrix}$$ 5. **Simplify fractions:** $$X = \begin{bmatrix}1 & 3 \\ 1 & -\frac{13}{2} \\ 5 & 0\end{bmatrix}$$ **Final answer:** $$X = \begin{bmatrix}1 & 3 \\ 1 & -\frac{13}{2} \\ 5 & 0\end{bmatrix}$$