https://file.aiquickdraw.com/mathbot/file/1726259022204339n40e8.jpg

The equation in the image consists of a matrix equation involving three 2x2 matrices. Let's break it down:

\[
\begin{bmatrix} 3 & 7 \\ 2 & 4 \end{bmatrix} + 2X = \begin{bmatrix} 1 & -5 \\ -4 & 6 \end{bmatrix}
\]

We need to solve for the matrix \(X\).

### Step 1: Isolate \(2X\)
Subtract the matrix on the left-hand side from both sides:

\[
2X = \begin{bmatrix} 1 & -5 \\ -4 & 6 \end{bmatrix} - \begin{bmatrix} 3 & 7 \\ 2 & 4 \end{bmatrix}
\]

### Step 2: Perform matrix subtraction
\[
2X = \begin{bmatrix} 1 - 3 & -5 - 7 \\ -4 - 2 & 6 - 4 \end{bmatrix}
= \begin{bmatrix} -2 & -12 \\ -6 & 2 \end{bmatrix}
\]

### Step 3: Divide by 2
Now divide the resulting matrix by 2 to find \(X\):

\[
X = \frac{1}{2} \begin{bmatrix} -2 & -12 \\ -6 & 2 \end{bmatrix}
= \begin{bmatrix} -1 & -6 \\ -3 & 1 \end{bmatrix}
\]

So, the solution is:

\[
X = \begin{bmatrix} -1 & -6 \\ -3 & 1 \end{bmatrix}
\]

Would you like a more detailed breakdown of any steps, or do you have any further questions?

Here are some related questions for further practice:
1. How do you perform matrix multiplication?
2. What happens if the matrices aren't the same size in matrix addition or subtraction?
3. Can a scalar be multiplied by a non-square matrix?
4. How can we verify if two matrices are inverses of each other?
5. What are some practical applications of matrix operations in computer science?

**Tip:** When performing matrix subtraction, always make sure to subtract corresponding elements from the same position in each matrix.

Solve the matrix equation: [3 7; 2 4] + 2X = [1 -5; -4 6]

Learn how to solve the matrix equation [3 7; 2 4] + 2X = [1 -5; -4 6]. This problem covers key mathematical concepts, including matrix subtraction and scalar multiplication. Suitable for students in Grades 9-12.

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