Finite Math Examples

$- 5 x - 6 i + 15 x = 13 - 19 i + 11 y i$

Step 1

Rewrite the equation as $13 - 19 i + 11 y i = - 5 x - 6 i + 15 x$ .

$13 - 19 i + 11 y i = - 5 x - 6 i + 15 x$

Step 2

Add $- 5 x$ and $15 x$ .

$13 - 19 i + 11 y i = 10 x - 6 i$

Step 3

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

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Step 3.1

Subtract $13$ from both sides of the equation.

$- 19 i + 11 y i = 10 x - 6 i - 13$

Step 3.2

Add $19 i$ to both sides of the equation.

$11 y i = 10 x - 6 i - 13 + 19 i$

Step 3.3

Add $- 6 i$ and $19 i$ .

$11 y i = 10 x - 13 + 13 i$

Step 4

Divide each term in $11 y i = 10 x - 13 + 13 i$ by $11 i$ and simplify.

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Step 4.1

Divide each term in $11 y i = 10 x - 13 + 13 i$ by $11 i$ .

$\frac{11 y i}{11 i} = \frac{10 x}{11 i} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $11$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{11 y i}{11 i} = \frac{10 x}{11 i} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.2.1.2

Rewrite the expression.

$\frac{y i}{i} = \frac{10 x}{11 i} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.2.2

Cancel the common factor of $i$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{y i}{i} = \frac{10 x}{11 i} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.2.2.2

Divide $y$ by $1$ .

$y = \frac{10 x}{11 i} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Multiply the numerator and denominator of $\frac{10 x}{11 i}$ by the conjugate of $11 i$ to make the denominator real.

$y = \frac{10 x}{11 i} \cdot \frac{i}{i} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.2

Multiply.

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Step 4.3.1.2.1

Combine.

$y = \frac{10 x i}{11 i i} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.2.2

Simplify the denominator.

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Step 4.3.1.2.2.1

Add parentheses.

$y = \frac{10 x i}{11 (i i)} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.2.2.2

Raise $i$ to the power of $1$ .

$y = \frac{10 x i}{11 (i^{1} i)} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.2.2.3

Raise $i$ to the power of $1$ .

$y = \frac{10 x i}{11 (i^{1} i^{1})} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.2.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{10 x i}{11 i^{1 + 1}} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.2.2.5

Add $1$ and $1$ .

$y = \frac{10 x i}{11 i^{2}} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.2.2.6

Rewrite $i^{2}$ as $- 1$ .

$y = \frac{10 x i}{11 \cdot - 1} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.3

Multiply $11$ by $- 1$ .

$y = \frac{10 x i}{- 11} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.4

Move the negative in front of the fraction.

$y = - \frac{10 x i}{11} + \frac{- 13}{11 i} + \frac{13 i}{11 i}$

Step 4.3.1.5

Multiply the numerator and denominator of $\frac{- 13}{11 i}$ by the conjugate of $11 i$ to make the denominator real.

$y = - \frac{10 x i}{11} + \frac{- 13}{11 i} \cdot \frac{i}{i} + \frac{13 i}{11 i}$

Step 4.3.1.6

Multiply.

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Step 4.3.1.6.1

Combine.

$y = - \frac{10 x i}{11} + \frac{- 13 i}{11 i i} + \frac{13 i}{11 i}$

Step 4.3.1.6.2

Simplify the denominator.

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Step 4.3.1.6.2.1

Add parentheses.

$y = - \frac{10 x i}{11} + \frac{- 13 i}{11 (i i)} + \frac{13 i}{11 i}$

Step 4.3.1.6.2.2

Raise $i$ to the power of $1$ .

$y = - \frac{10 x i}{11} + \frac{- 13 i}{11 (i^{1} i)} + \frac{13 i}{11 i}$

Step 4.3.1.6.2.3

Raise $i$ to the power of $1$ .

$y = - \frac{10 x i}{11} + \frac{- 13 i}{11 (i^{1} i^{1})} + \frac{13 i}{11 i}$

Step 4.3.1.6.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - \frac{10 x i}{11} + \frac{- 13 i}{11 i^{1 + 1}} + \frac{13 i}{11 i}$

Step 4.3.1.6.2.5

Add $1$ and $1$ .

$y = - \frac{10 x i}{11} + \frac{- 13 i}{11 i^{2}} + \frac{13 i}{11 i}$

Step 4.3.1.6.2.6

Rewrite $i^{2}$ as $- 1$ .

$y = - \frac{10 x i}{11} + \frac{- 13 i}{11 \cdot - 1} + \frac{13 i}{11 i}$

Step 4.3.1.7

Multiply $11$ by $- 1$ .

$y = - \frac{10 x i}{11} + \frac{- 13 i}{- 11} + \frac{13 i}{11 i}$

Step 4.3.1.8

Dividing two negative values results in a positive value.

$y = - \frac{10 x i}{11} + \frac{13 i}{11} + \frac{13 i}{11 i}$

Step 4.3.1.9

Cancel the common factor of $i$ .

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Step 4.3.1.9.1

Cancel the common factor.

$y = - \frac{10 x i}{11} + \frac{13 i}{11} + \frac{13 i}{11 i}$

Step 4.3.1.9.2

Rewrite the expression.

$y = - \frac{10 x i}{11} + \frac{13 i}{11} + \frac{13}{11}$