Finite Math Examples

$4 x - [\begin{array}{c} 1 & - 5 \\ 6 & 2 \end{array}] = [\begin{array}{c} - 2 & 11 \\ - 4 & - 6 \end{array}]$

Step 1

Move all terms not containing a variable to the right side.

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Step 1.1

Add $[\begin{array}{c} 1 & - 5 \\ 6 & 2 \end{array}]$ to both sides of the equation.

$4 x = [\begin{array}{c} - 2 & 11 \\ - 4 & - 6 \end{array}] + [\begin{array}{c} 1 & - 5 \\ 6 & 2 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Add the corresponding elements.

$4 x = [\begin{array}{c} - 2 + 1 & 11 - 5 \\ - 4 + 6 & - 6 + 2 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Add $- 2$ and $1$ .

$4 x = [\begin{array}{c} - 1 & 11 - 5 \\ - 4 + 6 & - 6 + 2 \end{array}]$

Step 2.2.2

Subtract $5$ from $11$ .

$4 x = [\begin{array}{c} - 1 & 6 \\ - 4 + 6 & - 6 + 2 \end{array}]$

Step 2.2.3

Add $- 4$ and $6$ .

$4 x = [\begin{array}{c} - 1 & 6 \\ 2 & - 6 + 2 \end{array}]$

Step 2.2.4

Add $- 6$ and $2$ .

$4 x = [\begin{array}{c} - 1 & 6 \\ 2 & - 4 \end{array}]$

Step 3

Multiply both sides by $\frac{1}{4}$ .

$\frac{1}{4} (4 x) = \frac{1}{4} [\begin{array}{c} - 1 & 6 \\ 2 & - 4 \end{array}]$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $4$ .

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Step 4.1.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{1}{4} [\begin{array}{c} - 1 & 6 \\ 2 & - 4 \end{array}]$

Step 4.1.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{1}{4} [\begin{array}{c} - 1 & 6 \\ 2 & - 4 \end{array}]$

Step 4.1.3

Rewrite the expression.

$x = \frac{1}{4} [\begin{array}{c} - 1 & 6 \\ 2 & - 4 \end{array}]$

Step 4.2

Multiply $\frac{1}{4}$ by each element of the matrix.

$x = [\begin{array}{c} \frac{1}{4} \cdot - 1 & \frac{1}{4} \cdot 6 \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3

Simplify each element in the matrix.

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Step 4.3.1

Combine $\frac{1}{4}$ and $- 1$ .

$x = [\begin{array}{c} \frac{- 1}{4} & \frac{1}{4} \cdot 6 \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.2

Move the negative in front of the fraction.

$x = [\begin{array}{c} - \frac{1}{4} & \frac{1}{4} \cdot 6 \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.3

Cancel the common factor of $2$ .

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Step 4.3.3.1

Factor $2$ out of $4$ .

$x = [\begin{array}{c} - \frac{1}{4} & \frac{1}{2 (2)} \cdot 6 \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.3.2

Factor $2$ out of $6$ .

$x = [\begin{array}{c} - \frac{1}{4} & \frac{1}{2 \cdot 2} \cdot (2 \cdot 3) \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.3.3

Cancel the common factor.

$x = [\begin{array}{c} - \frac{1}{4} & \frac{1}{2 \cdot 2} \cdot (2 \cdot 3) \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.3.4

Rewrite the expression.

$x = [\begin{array}{c} - \frac{1}{4} & \frac{1}{2} \cdot 3 \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.4

Combine $\frac{1}{2}$ and $3$ .

$x = [\begin{array}{c} - \frac{1}{4} & \frac{3}{2} \\ \frac{1}{4} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.5

Cancel the common factor of $2$ .

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Step 4.3.5.1

Factor $2$ out of $4$ .

$x = [\begin{array}{c} - \frac{1}{4} & \frac{3}{2} \\ \frac{1}{2 (2)} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.5.2

Cancel the common factor.

$x = [\begin{array}{c} - \frac{1}{4} & \frac{3}{2} \\ \frac{1}{2 \cdot 2} \cdot 2 & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.5.3

Rewrite the expression.

$x = [\begin{array}{c} - \frac{1}{4} & \frac{3}{2} \\ \frac{1}{2} & \frac{1}{4} \cdot - 4 \end{array}]$

Step 4.3.6

Cancel the common factor of $4$ .

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Step 4.3.6.1

Factor $4$ out of $- 4$ .

$x = [\begin{array}{c} - \frac{1}{4} & \frac{3}{2} \\ \frac{1}{2} & \frac{1}{4} \cdot (4 (- 1)) \end{array}]$

Step 4.3.6.2

Cancel the common factor.

$x = [\begin{array}{c} - \frac{1}{4} & \frac{3}{2} \\ \frac{1}{2} & \frac{1}{4} \cdot (4 \cdot - 1) \end{array}]$

Step 4.3.6.3

Rewrite the expression.

$x = [\begin{array}{c} - \frac{1}{4} & \frac{3}{2} \\ \frac{1}{2} & - 1 \end{array}]$