To solve the matrix equation $2X + A = B$ for $X$, we first need to isolate $X$.

Step-by-Step Solution:

1. Matrix Equation: $2X + A = B$

2. Isolate $X$: Subtract $A$ from both sides: $2X = B - A$

3. Divide by 2: $X = \frac{1}{2}(B - A)$

4. Substitute the Given Matrices for $A$ and $B$:

   $A = \begin{bmatrix} -2 & -7 \\ 0 & 7 \\ -3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 6 & -5 \\ 6 & 2 \\ 1 & 6 \end{bmatrix}$

5. Calculate $B - A$:

   = \begin{bmatrix} 8 & 2 \\ 6 & -5 \\ 4 & 2 \end{bmatrix}$$

6. Calculate $X$:

   = \begin{bmatrix} 4 & 1 \\ 3 & -2.5 \\ 2 & 1 \end{bmatrix}$$

Final Answer:

$X = \begin{bmatrix} 4 & 1 \\ 3 & -2.5 \\ 2 & 1 \end{bmatrix}$

Would you like any more details on any step or further explanations?

Here are some related questions you might find useful:

1. How do you perform matrix addition and subtraction?
2. How can scalar multiplication be applied to a matrix?
3. What properties of matrix operations are essential for solving matrix equations?
4. How would you solve a similar equation if $A$ and $B$ were square matrices?
5. What are some real-world applications of solving matrix equations?

Tip: Remember that in matrix operations, each element's position is crucial. The operations are carried out element-wise, which differs from traditional algebraic operations!