Algebra Examples

$22 (x + y i) + (28 + 4 i) = 72 - 62 i$

Step 1

Apply the distributive property.

$22 x + 22 y i + 28 + 4 i = 72 - 62 i$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $22 y i$ from both sides of the equation.

$22 x + 28 + 4 i = 72 - 62 i - 22 y i$

Step 2.2

Subtract $28$ from both sides of the equation.

$22 x + 4 i = 72 - 62 i - 22 y i - 28$

Step 2.3

Subtract $4 i$ from both sides of the equation.

$22 x = 72 - 62 i - 22 y i - 28 - 4 i$

Step 2.4

Subtract $28$ from $72$ .

$22 x = 44 - 62 i - 22 y i - 4 i$

Step 2.5

Subtract $4 i$ from $- 62 i$ .

$22 x = 44 - 22 y i - 66 i$

Step 3

Divide each term in $22 x = 44 - 22 y i - 66 i$ by $22$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $22 x = 44 - 22 y i - 66 i$ by $22$ .

$\frac{22 x}{22} = \frac{44}{22} + \frac{- 22 y i}{22} + \frac{- 66 i}{22}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $22$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{22 x}{22} = \frac{44}{22} + \frac{- 22 y i}{22} + \frac{- 66 i}{22}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{44}{22} + \frac{- 22 y i}{22} + \frac{- 66 i}{22}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Divide $44$ by $22$ .

$x = 2 + \frac{- 22 y i}{22} + \frac{- 66 i}{22}$

Step 3.3.1.2

Cancel the common factor of $- 22$ and $22$ .

Tap for more steps...

Step 3.3.1.2.1

Factor $22$ out of $- 22 y i$ .

$x = 2 + \frac{22 (- y i)}{22} + \frac{- 66 i}{22}$

Step 3.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.2.2.1

Factor $22$ out of $22$ .

$x = 2 + \frac{22 (- y i)}{22 (1)} + \frac{- 66 i}{22}$

Step 3.3.1.2.2.2

Cancel the common factor.

$x = 2 + \frac{22 (- y i)}{22 \cdot 1} + \frac{- 66 i}{22}$

Step 3.3.1.2.2.3

Rewrite the expression.

$x = 2 + \frac{- y i}{1} + \frac{- 66 i}{22}$

Step 3.3.1.2.2.4

Divide $- y i$ by $1$ .

$x = 2 - y i + \frac{- 66 i}{22}$

Step 3.3.1.3

Cancel the common factor of $- 66$ and $22$ .

Tap for more steps...

Step 3.3.1.3.1

Factor $22$ out of $- 66 i$ .

$x = 2 - y i + \frac{22 (- 3 i)}{22}$

Step 3.3.1.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.3.2.1

Factor $22$ out of $22$ .

$x = 2 - y i + \frac{22 (- 3 i)}{22 (1)}$

Step 3.3.1.3.2.2

Cancel the common factor.

$x = 2 - y i + \frac{22 (- 3 i)}{22 \cdot 1}$

Step 3.3.1.3.2.3

Rewrite the expression.

$x = 2 - y i + \frac{- 3 i}{1}$

Step 3.3.1.3.2.4

Divide $- 3 i$ by $1$ .

$x = 2 - y i - 3 i$