Algebra Examples

$3 x - 2 [\begin{array}{c} 1.5 & - 2.4 \\ 3.6 & - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 2$ by each element of the matrix.

$3 x + [\begin{array}{c} - 2 \cdot 1.5 & - 2 \cdot - 2.4 \\ - 2 \cdot 3.6 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $- 2$ by $1.5$ .

$3 x + [\begin{array}{c} - 3 & - 2 \cdot - 2.4 \\ - 2 \cdot 3.6 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Step 1.2.2

Multiply $- 2$ by $- 2.4$ .

$3 x + [\begin{array}{c} - 3 & 4.8 \\ - 2 \cdot 3.6 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Step 1.2.3

Multiply $- 2$ by $3.6$ .

$3 x + [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Step 1.2.4

Multiply $- 2$ by $- 0.5$ .

$3 x + [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Step 2

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

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Step 2.1

Subtract $[\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$ from both sides of the equation.

$3 x = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Subtract the corresponding elements.

$3 x = [\begin{array}{c} 1.2 + 3 & - 3.6 - 4.8 \\ 0.3 + 7.2 & 0.4 - 1 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Add $1.2$ and $3$ .

$3 x = [\begin{array}{c} 4.2 & - 3.6 - 4.8 \\ 0.3 + 7.2 & 0.4 - 1 \end{array}]$

Step 3.2.2

Subtract $4.8$ from $- 3.6$ .

$3 x = [\begin{array}{c} 4.2 & - 8.4 \\ 0.3 + 7.2 & 0.4 - 1 \end{array}]$

Step 3.2.3

Add $0.3$ and $7.2$ .

$3 x = [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & 0.4 - 1 \end{array}]$

Step 3.2.4

Subtract $1$ from $0.4$ .

$3 x = [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Step 4

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

$\frac{1}{3} (3 x) = \frac{1}{3} [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{1}{3} [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Step 5.1.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{1}{3} [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Step 5.1.3

Rewrite the expression.

$x = \frac{1}{3} [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Step 5.2

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

$x = [\begin{array}{c} \frac{1}{3} \cdot 4.2 & \frac{1}{3} \cdot - 8.4 \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Step 5.3

Simplify each element in the matrix.

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Step 5.3.1

Combine $\frac{1}{3}$ and $4.2$ .

$x = [\begin{array}{c} \frac{4.2}{3} & \frac{1}{3} \cdot - 8.4 \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Step 5.3.2

Divide $4.2$ by $3$ .

$x = [\begin{array}{c} 1.4 & \frac{1}{3} \cdot - 8.4 \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Step 5.3.3

Combine $\frac{1}{3}$ and $- 8.4$ .

$x = [\begin{array}{c} 1.4 & \frac{- 8.4}{3} \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Step 5.3.4

Divide $- 8.4$ by $3$ .

$x = [\begin{array}{c} 1.4 & - 2.8 \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Step 5.3.5

Combine $\frac{1}{3}$ and $7.5$ .

$x = [\begin{array}{c} 1.4 & - 2.8 \\ \frac{7.5}{3} & \frac{1}{3} \cdot - 0.6 \end{array}]$

Step 5.3.6

Divide $7.5$ by $3$ .

$x = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Step 5.3.7

Cancel the common factor of $0.6$ .

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Step 5.3.7.1

Factor $0.6$ out of $3$ .

$x = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & \frac{1}{0.6 (5)} \cdot - 0.6 \end{array}]$

Step 5.3.7.2

Factor $0.6$ out of $- 0.6$ .

$x = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & \frac{1}{0.6 \cdot 5} \cdot (0.6 \cdot - 1) \end{array}]$

Step 5.3.7.3

Cancel the common factor.

$x = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & \frac{1}{0.6 \cdot 5} \cdot (0.6 \cdot - 1) \end{array}]$

Step 5.3.7.4

Rewrite the expression.

$x = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & \frac{1}{5} \cdot - 1 \end{array}]$

Step 5.3.8

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

$x = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & \frac{- 1}{5} \end{array}]$

Step 5.3.9

Move the negative in front of the fraction.

$x = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & - \frac{1}{5} \end{array}]$