Algebra Examples

$4 x + [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] = [\begin{array}{c} 21 & 20 \\ 4 & 5 \end{array}]$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ from both sides of the equation.

$4 x = [\begin{array}{c} 21 & 20 \\ 4 & 5 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Subtract the corresponding elements.

$4 x = [\begin{array}{c} 21 - 1 & 20 - 0 \\ 4 - 0 & 5 - 1 \end{array}]$

Step 2.2

Simplify each element.

Tap for more steps...

Step 2.2.1

Subtract $1$ from $21$ .

$4 x = [\begin{array}{c} 20 & 20 - 0 \\ 4 - 0 & 5 - 1 \end{array}]$

Step 2.2.2

Subtract $0$ from $20$ .

$4 x = [\begin{array}{c} 20 & 20 \\ 4 - 0 & 5 - 1 \end{array}]$

Step 2.2.3

Subtract $0$ from $4$ .

$4 x = [\begin{array}{c} 20 & 20 \\ 4 & 5 - 1 \end{array}]$

Step 2.2.4

Subtract $1$ from $5$ .

$4 x = [\begin{array}{c} 20 & 20 \\ 4 & 4 \end{array}]$

Step 3

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

$\frac{1}{4} (4 x) = \frac{1}{4} [\begin{array}{c} 20 & 20 \\ 4 & 4 \end{array}]$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{1}{4} [\begin{array}{c} 20 & 20 \\ 4 & 4 \end{array}]$

Step 4.1.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{1}{4} [\begin{array}{c} 20 & 20 \\ 4 & 4 \end{array}]$

Step 4.1.3

Rewrite the expression.

$x = \frac{1}{4} [\begin{array}{c} 20 & 20 \\ 4 & 4 \end{array}]$

Step 4.2

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

$x = [\begin{array}{c} \frac{1}{4} \cdot 20 & \frac{1}{4} \cdot 20 \\ \frac{1}{4} \cdot 4 & \frac{1}{4} \cdot 4 \end{array}]$

Step 4.3

Simplify each element in the matrix.

Tap for more steps...

Step 4.3.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.3.1.1

Factor $4$ out of $20$ .

$x = [\begin{array}{c} \frac{1}{4} \cdot (4 (5)) & \frac{1}{4} \cdot 20 \\ \frac{1}{4} \cdot 4 & \frac{1}{4} \cdot 4 \end{array}]$

Step 4.3.1.2

Cancel the common factor.

$x = [\begin{array}{c} \frac{1}{4} \cdot (4 \cdot 5) & \frac{1}{4} \cdot 20 \\ \frac{1}{4} \cdot 4 & \frac{1}{4} \cdot 4 \end{array}]$

Step 4.3.1.3

Rewrite the expression.

$x = [\begin{array}{c} 5 & \frac{1}{4} \cdot 20 \\ \frac{1}{4} \cdot 4 & \frac{1}{4} \cdot 4 \end{array}]$

Step 4.3.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.3.2.1

Factor $4$ out of $20$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

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

Step 4.3.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.3.3.1

Cancel the common factor.

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

Step 4.3.3.2

Rewrite the expression.

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

Step 4.3.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.3.4.1

Cancel the common factor.

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

Step 4.3.4.2

Rewrite the expression.

$x = [\begin{array}{c} 5 & 5 \\ 1 & 1 \end{array}]$