Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $- 5$ by each element of the matrix.

$- 2 x + [\begin{array}{c} - 5 \cdot 2 & - 5 \cdot - 8 \\ - 5 \cdot - 4 & - 5 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $- 5$ by $2$ .

$- 2 x + [\begin{array}{c} - 10 & - 5 \cdot - 8 \\ - 5 \cdot - 4 & - 5 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.2

Multiply $- 5$ by $- 8$ .

$- 2 x + [\begin{array}{c} - 10 & 40 \\ - 5 \cdot - 4 & - 5 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.3

Multiply $- 5$ by $- 4$ .

$- 2 x + [\begin{array}{c} - 10 & 40 \\ 20 & - 5 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.4

Multiply $- 5$ by $2$ .

$- 2 x + [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2

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

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Step 2.1

Subtract $[\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$ from both sides of the equation.

$- 2 x = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 10 & 40 \\ 20 & - 10 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Subtract the corresponding elements.

$- 2 x = [\begin{array}{c} 4 + 10 & - 6 - 40 \\ 2 - 20 & - 8 + 10 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Add $4$ and $10$ .

$- 2 x = [\begin{array}{c} 14 & - 6 - 40 \\ 2 - 20 & - 8 + 10 \end{array}]$

Step 3.2.2

Subtract $40$ from $- 6$ .

$- 2 x = [\begin{array}{c} 14 & - 46 \\ 2 - 20 & - 8 + 10 \end{array}]$

Step 3.2.3

Subtract $20$ from $2$ .

$- 2 x = [\begin{array}{c} 14 & - 46 \\ - 18 & - 8 + 10 \end{array}]$

Step 3.2.4

Add $- 8$ and $10$ .

$- 2 x = [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 4

Multiply both sides by $- \frac{1}{2}$ .

$- \frac{1}{2} (- 2 x) = - \frac{1}{2} [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $2$ .

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Step 5.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} (- 2 x) = - \frac{1}{2} [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 5.1.2

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{1}{2} [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 5.1.3

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{1}{2} [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 5.1.4

Rewrite the expression.

$- - x = - \frac{1}{2} [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 5.2

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{1}{2} [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 5.3

Multiply $x$ by $1$ .

$x = - \frac{1}{2} [\begin{array}{c} 14 & - 46 \\ - 18 & 2 \end{array}]$

Step 5.4

Multiply $- \frac{1}{2}$ by each element of the matrix.

$x = [\begin{array}{c} - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5

Simplify each element in the matrix.

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Step 5.5.1

Cancel the common factor of $2$ .

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Step 5.5.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} \frac{- 1}{2} \cdot 14 & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.1.2

Factor $2$ out of $14$ .

$x = [\begin{array}{c} \frac{- 1}{2} \cdot (2 (7)) & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.1.3

Cancel the common factor.

$x = [\begin{array}{c} \frac{- 1}{2} \cdot (2 \cdot 7) & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.1.4

Rewrite the expression.

$x = [\begin{array}{c} - 1 \cdot 7 & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.2

Multiply $- 1$ by $7$ .

$x = [\begin{array}{c} - 7 & - \frac{1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.3

Cancel the common factor of $2$ .

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Step 5.5.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} - 7 & \frac{- 1}{2} \cdot - 46 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.3.2

Factor $2$ out of $- 46$ .

$x = [\begin{array}{c} - 7 & \frac{- 1}{2} \cdot (2 (- 23)) \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.3.3

Cancel the common factor.

$x = [\begin{array}{c} - 7 & \frac{- 1}{2} \cdot (2 \cdot - 23) \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.3.4

Rewrite the expression.

$x = [\begin{array}{c} - 7 & - 1 \cdot - 23 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.4

Multiply $- 1$ by $- 23$ .

$x = [\begin{array}{c} - 7 & 23 \\ - \frac{1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.5

Cancel the common factor of $2$ .

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Step 5.5.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} - 7 & 23 \\ \frac{- 1}{2} \cdot - 18 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.5.2

Factor $2$ out of $- 18$ .

$x = [\begin{array}{c} - 7 & 23 \\ \frac{- 1}{2} \cdot (2 (- 9)) & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.5.3

Cancel the common factor.

$x = [\begin{array}{c} - 7 & 23 \\ \frac{- 1}{2} \cdot (2 \cdot - 9) & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.5.4

Rewrite the expression.

$x = [\begin{array}{c} - 7 & 23 \\ - 1 \cdot - 9 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.6

Multiply $- 1$ by $- 9$ .

$x = [\begin{array}{c} - 7 & 23 \\ 9 & - \frac{1}{2} \cdot 2 \end{array}]$

Step 5.5.7

Cancel the common factor of $2$ .

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Step 5.5.7.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} - 7 & 23 \\ 9 & \frac{- 1}{2} \cdot 2 \end{array}]$

Step 5.5.7.2

Cancel the common factor.

$x = [\begin{array}{c} - 7 & 23 \\ 9 & \frac{- 1}{2} \cdot 2 \end{array}]$

Step 5.5.7.3

Rewrite the expression.

$x = [\begin{array}{c} - 7 & 23 \\ 9 & - 1 \end{array}]$