Precalculus Examples

$- \frac{1}{3} x - [\begin{array}{c} 3 & 6 & 2 \\ 9 & 1 & 7 \end{array}] = [\begin{array}{c} - 8 & 3 & - 1 \\ 12 & - 4 & - 3 \end{array}]$

Step 1

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

$- \frac{x}{3} - [\begin{array}{c} 3 & 6 & 2 \\ 9 & 1 & 7 \end{array}] = [\begin{array}{c} - 8 & 3 & - 1 \\ 12 & - 4 & - 3 \end{array}]$

Step 2

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

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Step 2.1

Add $[\begin{array}{c} 3 & 6 & 2 \\ 9 & 1 & 7 \end{array}]$ to both sides of the equation.

$- \frac{x}{3} = [\begin{array}{c} - 8 & 3 & - 1 \\ 12 & - 4 & - 3 \end{array}] + [\begin{array}{c} 3 & 6 & 2 \\ 9 & 1 & 7 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Add the corresponding elements.

$- \frac{x}{3} = [\begin{array}{c} - 8 + 3 & 3 + 6 & - 1 + 2 \\ 12 + 9 & - 4 + 1 & - 3 + 7 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Add $- 8$ and $3$ .

$- \frac{x}{3} = [\begin{array}{c} - 5 & 3 + 6 & - 1 + 2 \\ 12 + 9 & - 4 + 1 & - 3 + 7 \end{array}]$

Step 3.2.2

Add $3$ and $6$ .

$- \frac{x}{3} = [\begin{array}{c} - 5 & 9 & - 1 + 2 \\ 12 + 9 & - 4 + 1 & - 3 + 7 \end{array}]$

Step 3.2.3

Add $- 1$ and $2$ .

$- \frac{x}{3} = [\begin{array}{c} - 5 & 9 & 1 \\ 12 + 9 & - 4 + 1 & - 3 + 7 \end{array}]$

Step 3.2.4

Add $12$ and $9$ .

$- \frac{x}{3} = [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 4 + 1 & - 3 + 7 \end{array}]$

Step 3.2.5

Add $- 4$ and $1$ .

$- \frac{x}{3} = [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & - 3 + 7 \end{array}]$

Step 3.2.6

Add $- 3$ and $7$ .

$- \frac{x}{3} = [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 4

Multiply both sides by $- 3$ .

$- 3 (- \frac{x}{3}) = - 3 [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 3 \frac{- x}{3} = - 3 [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 5.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x}{3} = - 3 [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 5.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 5.1.4

Rewrite the expression.

$- - x = - 3 [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 5.2

Multiply $- 1$ by $- 1$ .

$1 x = - 3 [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 5.3

Multiply $x$ by $1$ .

$x = - 3 [\begin{array}{c} - 5 & 9 & 1 \\ 21 & - 3 & 4 \end{array}]$

Step 5.4

Multiply $- 3$ by each element of the matrix.

$x = [\begin{array}{c} - 3 \cdot - 5 & - 3 \cdot 9 & - 3 \cdot 1 \\ - 3 \cdot 21 & - 3 \cdot - 3 & - 3 \cdot 4 \end{array}]$

Step 5.5

Simplify each element in the matrix.

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Step 5.5.1

Multiply $- 3$ by $- 5$ .

$x = [\begin{array}{c} 15 & - 3 \cdot 9 & - 3 \cdot 1 \\ - 3 \cdot 21 & - 3 \cdot - 3 & - 3 \cdot 4 \end{array}]$

Step 5.5.2

Multiply $- 3$ by $9$ .

$x = [\begin{array}{c} 15 & - 27 & - 3 \cdot 1 \\ - 3 \cdot 21 & - 3 \cdot - 3 & - 3 \cdot 4 \end{array}]$

Step 5.5.3

Multiply $- 3$ by $1$ .

$x = [\begin{array}{c} 15 & - 27 & - 3 \\ - 3 \cdot 21 & - 3 \cdot - 3 & - 3 \cdot 4 \end{array}]$

Step 5.5.4

Multiply $- 3$ by $21$ .

$x = [\begin{array}{c} 15 & - 27 & - 3 \\ - 63 & - 3 \cdot - 3 & - 3 \cdot 4 \end{array}]$

Step 5.5.5

Multiply $- 3$ by $- 3$ .

$x = [\begin{array}{c} 15 & - 27 & - 3 \\ - 63 & 9 & - 3 \cdot 4 \end{array}]$

Step 5.5.6

Multiply $- 3$ by $4$ .

$x = [\begin{array}{c} 15 & - 27 & - 3 \\ - 63 & 9 & - 12 \end{array}]$