Pre-Algebra Examples

$(2 x + 1) + 3 i = 0 - 13 + i (9 + y)$

Step 1

Simplify $0 - 13 + i (9 + y)$ .

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Step 1.1

Subtract $13$ from $0$ .

$2 x + 1 + 3 i = - 13 + i (9 + y)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$2 x + 1 + 3 i = - 13 + i \cdot 9 + i y$

Step 1.2.2

Move $9$ to the left of $i$ .

$2 x + 1 + 3 i = - 13 + 9 i + i y$

Step 2

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

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Step 2.1

Subtract $1$ from both sides of the equation.

$2 x + 3 i = - 13 + 9 i + i y - 1$

Step 2.2

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

$2 x = - 13 + 9 i + i y - 1 - 3 i$

Step 2.3

Subtract $1$ from $- 13$ .

$2 x = - 14 + 9 i + i y - 3 i$

Step 2.4

Subtract $3 i$ from $9 i$ .

$2 x = - 14 + i y + 6 i$

Step 3

Divide each term in $2 x = - 14 + i y + 6 i$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x = - 14 + i y + 6 i$ by $2$ .

$\frac{2 x}{2} = \frac{- 14}{2} + \frac{i y}{2} + \frac{6 i}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 14}{2} + \frac{i y}{2} + \frac{6 i}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{2} + \frac{i y}{2} + \frac{6 i}{2}$

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 $- 14$ by $2$ .

$x = - 7 + \frac{i y}{2} + \frac{6 i}{2}$

Step 3.3.1.2

Cancel the common factor of $6$ and $2$ .

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Step 3.3.1.2.1

Factor $2$ out of $6 i$ .

$x = - 7 + \frac{i y}{2} + \frac{2 (3 i)}{2}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $2$ out of $2$ .

$x = - 7 + \frac{i y}{2} + \frac{2 (3 i)}{2 (1)}$

Step 3.3.1.2.2.2

Cancel the common factor.

$x = - 7 + \frac{i y}{2} + \frac{2 (3 i)}{2 \cdot 1}$

Step 3.3.1.2.2.3

Rewrite the expression.

$x = - 7 + \frac{i y}{2} + \frac{3 i}{1}$

Step 3.3.1.2.2.4

Divide $3 i$ by $1$ .

$x = - 7 + \frac{i y}{2} + 3 i$