Precalculus Examples

$[\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}] = [\begin{array}{c} 8 & - 5 & 2 & - 1 \end{array}] - 3 X$

Step 1

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

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Step 1.1

Subtract $[\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}]$ from both sides of the equation.

$0 = [\begin{array}{c} 8 & - 5 & 2 & - 1 \end{array}] - 3 X - [\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}]$

Step 2

Move all terms containing a variable to the left side.

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Step 2.1

Add $3 X$ to both sides of the equation.

$3 X = [\begin{array}{c} 8 & - 5 & 2 & - 1 \end{array}] - [\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}]$

Step 3

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

$\frac{1}{3} (3 X) = \frac{1}{3} ([\begin{array}{c} 8 & - 5 & 2 & - 1 \end{array}] - [\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}])$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $3$ .

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Step 4.1.1

Factor $3$ out of $3 X$ .

$\frac{1}{3} (3 (X)) = \frac{1}{3} ([\begin{array}{c} 8 & - 5 & 2 & - 1 \end{array}] - [\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}])$

Step 4.1.2

Cancel the common factor.

$\frac{1}{3} (3 X) = \frac{1}{3} ([\begin{array}{c} 8 & - 5 & 2 & - 1 \end{array}] - [\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}])$

Step 4.1.3

Rewrite the expression.

$X = \frac{1}{3} ([\begin{array}{c} 8 & - 5 & 2 & - 1 \end{array}] - [\begin{array}{c} - 4 & 10 & 35 & - 34 \end{array}])$

Step 4.2

Subtract the corresponding elements.

$X = \frac{1}{3} [\begin{array}{c} 8 + 4 & - 5 - 10 & 2 - 35 & - 1 + 34 \end{array}]$

Step 4.3

Simplify each element.

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Step 4.3.1

Add $8$ and $4$ .

$X = \frac{1}{3} [\begin{array}{c} 12 & - 5 - 10 & 2 - 35 & - 1 + 34 \end{array}]$

Step 4.3.2

Subtract $10$ from $- 5$ .

$X = \frac{1}{3} [\begin{array}{c} 12 & - 15 & 2 - 35 & - 1 + 34 \end{array}]$

Step 4.3.3

Subtract $35$ from $2$ .

$X = \frac{1}{3} [\begin{array}{c} 12 & - 15 & - 33 & - 1 + 34 \end{array}]$

Step 4.3.4

Add $- 1$ and $34$ .

$X = \frac{1}{3} [\begin{array}{c} 12 & - 15 & - 33 & 33 \end{array}]$

Step 4.4

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

$X = [\begin{array}{c} \frac{1}{3} \cdot 12 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot - 33 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5

Simplify each element in the matrix.

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Step 4.5.1

Cancel the common factor of $3$ .

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Step 4.5.1.1

Factor $3$ out of $12$ .

$X = [\begin{array}{c} \frac{1}{3} \cdot (3 (4)) & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot - 33 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.1.2

Cancel the common factor.

$X = [\begin{array}{c} \frac{1}{3} \cdot (3 \cdot 4) & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot - 33 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.1.3

Rewrite the expression.

$X = [\begin{array}{c} 4 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot - 33 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.2

Cancel the common factor of $3$ .

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Step 4.5.2.1

Factor $3$ out of $- 15$ .

$X = [\begin{array}{c} 4 & \frac{1}{3} \cdot (3 (- 5)) & \frac{1}{3} \cdot - 33 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.2.2

Cancel the common factor.

$X = [\begin{array}{c} 4 & \frac{1}{3} \cdot (3 \cdot - 5) & \frac{1}{3} \cdot - 33 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.2.3

Rewrite the expression.

$X = [\begin{array}{c} 4 & - 5 & \frac{1}{3} \cdot - 33 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.3

Cancel the common factor of $3$ .

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Step 4.5.3.1

Factor $3$ out of $- 33$ .

$X = [\begin{array}{c} 4 & - 5 & \frac{1}{3} \cdot (3 (- 11)) & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.3.2

Cancel the common factor.

$X = [\begin{array}{c} 4 & - 5 & \frac{1}{3} \cdot (3 \cdot - 11) & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.3.3

Rewrite the expression.

$X = [\begin{array}{c} 4 & - 5 & - 11 & \frac{1}{3} \cdot 33 \end{array}]$

Step 4.5.4

Cancel the common factor of $3$ .

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Step 4.5.4.1

Factor $3$ out of $33$ .

$X = [\begin{array}{c} 4 & - 5 & - 11 & \frac{1}{3} \cdot (3 (11)) \end{array}]$

Step 4.5.4.2

Cancel the common factor.

$X = [\begin{array}{c} 4 & - 5 & - 11 & \frac{1}{3} \cdot (3 \cdot 11) \end{array}]$

Step 4.5.4.3

Rewrite the expression.

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