Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $[\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}]$ from both sides of the equation.

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

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

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

Step 2.2

Simplify each element.

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Step 2.2.1

Subtract $2$ from $2$ .

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

Step 2.2.2

Subtract $5$ from $- 2$ .

$2 x = [\begin{array}{c} 0 & - 7 \\ 3 - 5 & 5 + 4 \end{array}]$

Step 2.2.3

Subtract $5$ from $3$ .

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

Step 2.2.4

Add $5$ and $4$ .

$2 x = [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Step 3

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

$\frac{1}{2} (2 x) = \frac{1}{2} [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{1}{2} [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Step 4.1.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{1}{2} [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Step 4.1.3

Rewrite the expression.

$x = \frac{1}{2} [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Step 4.2

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

$x = [\begin{array}{c} \frac{1}{2} \cdot 0 & \frac{1}{2} \cdot - 7 \\ \frac{1}{2} \cdot - 2 & \frac{1}{2} \cdot 9 \end{array}]$

Step 4.3

Simplify each element in the matrix.

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Step 4.3.1

Multiply $\frac{1}{2}$ by $0$ .

$x = [\begin{array}{c} 0 & \frac{1}{2} \cdot - 7 \\ \frac{1}{2} \cdot - 2 & \frac{1}{2} \cdot 9 \end{array}]$

Step 4.3.2

Combine $\frac{1}{2}$ and $- 7$ .

$x = [\begin{array}{c} 0 & \frac{- 7}{2} \\ \frac{1}{2} \cdot - 2 & \frac{1}{2} \cdot 9 \end{array}]$

Step 4.3.3

Move the negative in front of the fraction.

$x = [\begin{array}{c} 0 & - \frac{7}{2} \\ \frac{1}{2} \cdot - 2 & \frac{1}{2} \cdot 9 \end{array}]$

Step 4.3.4

Cancel the common factor of $2$ .

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Step 4.3.4.1

Factor $2$ out of $- 2$ .

$x = [\begin{array}{c} 0 & - \frac{7}{2} \\ \frac{1}{2} \cdot (2 (- 1)) & \frac{1}{2} \cdot 9 \end{array}]$

Step 4.3.4.2

Cancel the common factor.

$x = [\begin{array}{c} 0 & - \frac{7}{2} \\ \frac{1}{2} \cdot (2 \cdot - 1) & \frac{1}{2} \cdot 9 \end{array}]$

Step 4.3.4.3

Rewrite the expression.

$x = [\begin{array}{c} 0 & - \frac{7}{2} \\ - 1 & \frac{1}{2} \cdot 9 \end{array}]$

Step 4.3.5

Combine $\frac{1}{2}$ and $9$ .

$x = [\begin{array}{c} 0 & - \frac{7}{2} \\ - 1 & \frac{9}{2} \end{array}]$