Algebra Examples

$3 x - 11 + (3 - 2 y) i = 4 - i$

Step 1

Apply the distributive property.

$3 x - 11 + 3 i - 2 y i = 4 - i$

Step 2

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

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Step 2.1

Add $11$ to both sides of the equation.

$3 x + 3 i - 2 y i = 4 - i + 11$

Step 2.2

Subtract $3 i$ from both sides of the equation.

$3 x - 2 y i = 4 - i + 11 - 3 i$

Step 2.3

Add $2 y i$ to both sides of the equation.

$3 x = 4 - i + 11 - 3 i + 2 y i$

Step 2.4

Add $4$ and $11$ .

$3 x = 15 - i - 3 i + 2 y i$

Step 2.5

Subtract $3 i$ from $- i$ .

$3 x = 15 - 4 i + 2 y i$

Step 3

Divide each term in $3 x = 15 - 4 i + 2 y i$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = 15 - 4 i + 2 y i$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3} + \frac{- 4 i}{3} + \frac{2 y i}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3} + \frac{- 4 i}{3} + \frac{2 y i}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{3} + \frac{- 4 i}{3} + \frac{2 y i}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $15$ by $3$ .

$x = 5 + \frac{- 4 i}{3} + \frac{2 y i}{3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$x = 5 - \frac{4 i}{3} + \frac{2 y i}{3}$