Precalculus Examples

$\frac{1}{5} x + [\begin{array}{c} 4 & 7 \\ 2 & 1 \\ 8 & 6 \end{array}] = [\begin{array}{c} 9 & - 4 \\ - 2 & 8 \\ - 3 & 7 \end{array}]$

Step 1

Combine $\frac{1}{5}$ and $x$ .

$\frac{x}{5} + [\begin{array}{c} 4 & 7 \\ 2 & 1 \\ 8 & 6 \end{array}] = [\begin{array}{c} 9 & - 4 \\ - 2 & 8 \\ - 3 & 7 \end{array}]$

Step 2

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

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Step 2.1

Subtract $[\begin{array}{c} 4 & 7 \\ 2 & 1 \\ 8 & 6 \end{array}]$ from both sides of the equation.

$\frac{x}{5} = [\begin{array}{c} 9 & - 4 \\ - 2 & 8 \\ - 3 & 7 \end{array}] - [\begin{array}{c} 4 & 7 \\ 2 & 1 \\ 8 & 6 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Subtract the corresponding elements.

$\frac{x}{5} = [\begin{array}{c} 9 - 4 & - 4 - 7 \\ - 2 - 2 & 8 - 1 \\ - 3 - 8 & 7 - 6 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Subtract $4$ from $9$ .

$\frac{x}{5} = [\begin{array}{c} 5 & - 4 - 7 \\ - 2 - 2 & 8 - 1 \\ - 3 - 8 & 7 - 6 \end{array}]$

Step 3.2.2

Subtract $7$ from $- 4$ .

$\frac{x}{5} = [\begin{array}{c} 5 & - 11 \\ - 2 - 2 & 8 - 1 \\ - 3 - 8 & 7 - 6 \end{array}]$

Step 3.2.3

Subtract $2$ from $- 2$ .

$\frac{x}{5} = [\begin{array}{c} 5 & - 11 \\ - 4 & 8 - 1 \\ - 3 - 8 & 7 - 6 \end{array}]$

Step 3.2.4

Subtract $1$ from $8$ .

$\frac{x}{5} = [\begin{array}{c} 5 & - 11 \\ - 4 & 7 \\ - 3 - 8 & 7 - 6 \end{array}]$

Step 3.2.5

Subtract $8$ from $- 3$ .

$\frac{x}{5} = [\begin{array}{c} 5 & - 11 \\ - 4 & 7 \\ - 11 & 7 - 6 \end{array}]$

Step 3.2.6

Subtract $6$ from $7$ .

$\frac{x}{5} = [\begin{array}{c} 5 & - 11 \\ - 4 & 7 \\ - 11 & 1 \end{array}]$

Step 4

Multiply both sides by $5$ .

$5 \frac{x}{5} = 5 [\begin{array}{c} 5 & - 11 \\ - 4 & 7 \\ - 11 & 1 \end{array}]$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $5$ .

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Step 5.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 [\begin{array}{c} 5 & - 11 \\ - 4 & 7 \\ - 11 & 1 \end{array}]$

Step 5.1.2

Rewrite the expression.

$x = 5 [\begin{array}{c} 5 & - 11 \\ - 4 & 7 \\ - 11 & 1 \end{array}]$

Step 5.2

Multiply $5$ by each element of the matrix.

$x = [\begin{array}{c} 5 \cdot 5 & 5 \cdot - 11 \\ 5 \cdot - 4 & 5 \cdot 7 \\ 5 \cdot - 11 & 5 \cdot 1 \end{array}]$

Step 5.3

Simplify each element in the matrix.

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Step 5.3.1

Multiply $5$ by $5$ .

$x = [\begin{array}{c} 25 & 5 \cdot - 11 \\ 5 \cdot - 4 & 5 \cdot 7 \\ 5 \cdot - 11 & 5 \cdot 1 \end{array}]$

Step 5.3.2

Multiply $5$ by $- 11$ .

$x = [\begin{array}{c} 25 & - 55 \\ 5 \cdot - 4 & 5 \cdot 7 \\ 5 \cdot - 11 & 5 \cdot 1 \end{array}]$

Step 5.3.3

Multiply $5$ by $- 4$ .

$x = [\begin{array}{c} 25 & - 55 \\ - 20 & 5 \cdot 7 \\ 5 \cdot - 11 & 5 \cdot 1 \end{array}]$

Step 5.3.4

Multiply $5$ by $7$ .

$x = [\begin{array}{c} 25 & - 55 \\ - 20 & 35 \\ 5 \cdot - 11 & 5 \cdot 1 \end{array}]$

Step 5.3.5

Multiply $5$ by $- 11$ .

$x = [\begin{array}{c} 25 & - 55 \\ - 20 & 35 \\ - 55 & 5 \cdot 1 \end{array}]$

Step 5.3.6

Multiply $5$ by $1$ .

$x = [\begin{array}{c} 25 & - 55 \\ - 20 & 35 \\ - 55 & 5 \end{array}]$