Algebra Examples

$4 x + [\begin{array}{c} 6 & - 6 \\ - 8 & 0 \\ 11 & 7 \end{array}] = [\begin{array}{c} 11 & 0 \\ 0 & - 2 \\ 6 & 7 \end{array}]$

Step 1

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

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Step 1.1

Subtract $[\begin{array}{c} 6 & - 6 \\ - 8 & 0 \\ 11 & 7 \end{array}]$ from both sides of the equation.

$4 x = [\begin{array}{c} 11 & 0 \\ 0 & - 2 \\ 6 & 7 \end{array}] - [\begin{array}{c} 6 & - 6 \\ - 8 & 0 \\ 11 & 7 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

$4 x = [\begin{array}{c} 11 - 6 & 0 + 6 \\ 0 + 8 & - 2 - 0 \\ 6 - 11 & 7 - 7 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Subtract $6$ from $11$ .

$4 x = [\begin{array}{c} 5 & 0 + 6 \\ 0 + 8 & - 2 - 0 \\ 6 - 11 & 7 - 7 \end{array}]$

Step 2.2.2

Add $0$ and $6$ .

$4 x = [\begin{array}{c} 5 & 6 \\ 0 + 8 & - 2 - 0 \\ 6 - 11 & 7 - 7 \end{array}]$

Step 2.2.3

Add $0$ and $8$ .

$4 x = [\begin{array}{c} 5 & 6 \\ 8 & - 2 - 0 \\ 6 - 11 & 7 - 7 \end{array}]$

Step 2.2.4

Subtract $0$ from $- 2$ .

$4 x = [\begin{array}{c} 5 & 6 \\ 8 & - 2 \\ 6 - 11 & 7 - 7 \end{array}]$

Step 2.2.5

Subtract $11$ from $6$ .

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

Step 2.2.6

Subtract $7$ from $7$ .

$4 x = [\begin{array}{c} 5 & 6 \\ 8 & - 2 \\ - 5 & 0 \end{array}]$

Step 3

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

$\frac{1}{4} (4 x) = \frac{1}{4} [\begin{array}{c} 5 & 6 \\ 8 & - 2 \\ - 5 & 0 \end{array}]$

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 $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{1}{4} [\begin{array}{c} 5 & 6 \\ 8 & - 2 \\ - 5 & 0 \end{array}]$

Step 4.1.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{1}{4} [\begin{array}{c} 5 & 6 \\ 8 & - 2 \\ - 5 & 0 \end{array}]$

Step 4.1.3

Rewrite the expression.

$x = \frac{1}{4} [\begin{array}{c} 5 & 6 \\ 8 & - 2 \\ - 5 & 0 \end{array}]$

Step 4.2

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

$x = [\begin{array}{c} \frac{1}{4} \cdot 5 & \frac{1}{4} \cdot 6 \\ \frac{1}{4} \cdot 8 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3

Simplify each element in the matrix.

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Step 4.3.1

Combine $\frac{1}{4}$ and $5$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{1}{4} \cdot 6 \\ \frac{1}{4} \cdot 8 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.2

Cancel the common factor of $2$ .

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Step 4.3.2.1

Factor $2$ out of $4$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{1}{2 (2)} \cdot 6 \\ \frac{1}{4} \cdot 8 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.2.2

Factor $2$ out of $6$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{1}{2 \cdot 2} \cdot (2 \cdot 3) \\ \frac{1}{4} \cdot 8 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.2.3

Cancel the common factor.

$x = [\begin{array}{c} \frac{5}{4} & \frac{1}{2 \cdot 2} \cdot (2 \cdot 3) \\ \frac{1}{4} \cdot 8 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.2.4

Rewrite the expression.

$x = [\begin{array}{c} \frac{5}{4} & \frac{1}{2} \cdot 3 \\ \frac{1}{4} \cdot 8 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.3

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

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ \frac{1}{4} \cdot 8 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.4

Cancel the common factor of $4$ .

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Step 4.3.4.1

Factor $4$ out of $8$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ \frac{1}{4} \cdot (4 (2)) & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.4.2

Cancel the common factor.

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ \frac{1}{4} \cdot (4 \cdot 2) & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.4.3

Rewrite the expression.

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & \frac{1}{4} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.5

Cancel the common factor of $2$ .

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Step 4.3.5.1

Factor $2$ out of $4$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & \frac{1}{2 (2)} \cdot - 2 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.5.2

Factor $2$ out of $- 2$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & \frac{1}{2 \cdot 2} \cdot (2 \cdot - 1) \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.5.3

Cancel the common factor.

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & \frac{1}{2 \cdot 2} \cdot (2 \cdot - 1) \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.5.4

Rewrite the expression.

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & \frac{1}{2} \cdot - 1 \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.6

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

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & \frac{- 1}{2} \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.7

Move the negative in front of the fraction.

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & - \frac{1}{2} \\ \frac{1}{4} \cdot - 5 & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.8

Combine $\frac{1}{4}$ and $- 5$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & - \frac{1}{2} \\ \frac{- 5}{4} & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.9

Move the negative in front of the fraction.

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & - \frac{1}{2} \\ - \frac{5}{4} & \frac{1}{4} \cdot 0 \end{array}]$

Step 4.3.10

Multiply $\frac{1}{4}$ by $0$ .

$x = [\begin{array}{c} \frac{5}{4} & \frac{3}{2} \\ 2 & - \frac{1}{2} \\ - \frac{5}{4} & 0 \end{array}]$