Solve for [tex]x[/tex].

[tex]\[ 3x = 6x - 2 \][/tex]



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[tex]$\begin{array}{r}\left(\begin{array}{ccc}-8 & -3 & 1 \\ 5 & -2 & -8 \\ 4 & 0 & 12\end{array}\right)+\left(\begin{array}{ccc}-5 & 1 & -11 \\ -4 & 0 & -15 \\ 3 & 10 & 21\end{array}\right)\end{array}$[/tex]
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Response:



Answer :

Let's solve the problem step-by-step.

We need to perform the following operations on the given matrices:
1. Add the corresponding elements of the two matrices.
2. Subtract 30 from each resulting element.

The given matrices are:

[tex]\[ \mathbf{A} = \begin{pmatrix} -8 & -3 & 1 \\ 5 & -2 & -8 \\ 4 & 0 & 12 \end{pmatrix} \][/tex]

[tex]\[ \mathbf{B} = \begin{pmatrix} -5 & 1 & -11 \\ -4 & 0 & -15 \\ 3 & 10 & 21 \end{pmatrix} \][/tex]

### Step 1: Add corresponding elements of matrices A and B
Let's compute the addition of matrices [tex]\(\mathbf{A}\)[/tex] and [tex]\(\mathbf{B}\)[/tex]:

[tex]\[ \mathbf{A} + \mathbf{B} = \begin{pmatrix} -8 + (-5) & -3 + 1 & 1 + (-11) \\ 5 + (-4) & -2 + 0 & -8 + (-15) \\ 4 + 3 & 0 + 10 & 12 + 21 \end{pmatrix} \][/tex]

Calculating each element:

[tex]\[ \mathbf{A} + \mathbf{B} = \begin{pmatrix} -8 - 5 & -3 + 1 & 1 - 11 \\ 5 - 4 & -2 + 0 & -8 - 15 \\ 4 + 3 & 0 + 10 & 12 + 21 \end{pmatrix} = \begin{pmatrix} -13 & -2 & -10 \\ 1 & -2 & -23 \\ 7 & 10 & 33 \end{pmatrix} \][/tex]

### Step 2: Subtract 30 from each element
Next, we subtract 30 from every element of the resultant matrix:

[tex]\[ \mathbf{Result} = \begin{pmatrix} -13 - 30 & -2 - 30 & -10 - 30 \\ 1 - 30 & -2 - 30 & -23 - 30 \\ 7 - 30 & 10 - 30 & 33 - 30 \end{pmatrix} = \begin{pmatrix} -43 & -32 & -40 \\ -29 & -32 & -53 \\ -23 & -20 & 3 \end{pmatrix} \][/tex]

So, the final result is:

[tex]\[ \begin{pmatrix} -43 & -32 & -40 \\ -29 & -32 & -53 \\ -23 & -20 & 3 \end{pmatrix} \][/tex]