Finite Math Examples

$3 x = [\begin{array}{c} - 3 \\ 7 \end{array}] - [\begin{array}{c} - 1 \\ 4 \end{array}]$

Step 1

Simplify the right side of the equation.

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Subtract the corresponding elements.

$3 X = [\begin{array}{c} - 3 - (- 1) \\ 7 - 4 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 3 - (- 1) \\ 7 - 4 \end{array}]$ .

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Simplify $- 3 - (- 1)$ .

$3 X = [\begin{array}{c} - 2 \\ 7 - 4 \end{array}]$

Simplify $7 - 4$ .

$3 X = [\begin{array}{c} - 2 \\ 3 \end{array}]$

Step 2

Multiply both sides of the equation by $\frac{1}{3}$ .

$\frac{1}{3} \cdot (3 X) = \frac{1}{3} \cdot [\begin{array}{c} - 2 \\ 3 \end{array}]$

Step 3

Simplify both sides of the equation.

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Cancel the common factor of $3$ .

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Factor $3$ out of $3 X$ .

$\frac{1}{3} \cdot (3 (X)) = \frac{1}{3} \cdot [\begin{array}{c} - 2 \\ 3 \end{array}]$

Cancel the common factor.

$\frac{1}{3} \cdot (3 X) = \frac{1}{3} \cdot [\begin{array}{c} - 2 \\ 3 \end{array}]$

Rewrite the expression.

$X = \frac{1}{3} \cdot [\begin{array}{c} - 2 \\ 3 \end{array}]$

Simplify the right side of the equation.

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Multiply $\frac{1}{3}$ by each element of the matrix.

$X = [\begin{array}{c} \frac{1}{3} \cdot - 2 \\ \frac{1}{3} \cdot 3 \end{array}]$

Simplify each element in the matrix.

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Rearrange $\frac{1}{3} \cdot - 2$ .

$X = [\begin{array}{c} - \frac{2}{3} \\ \frac{1}{3} \cdot 3 \end{array}]$

Rearrange $\frac{1}{3} \cdot 3$ .

$X = [\begin{array}{c} - \frac{2}{3} \\ 1 \end{array}]$