Basic Math Examples

$- 9 x + 8 i = - 54 + (16 y) i$

Step 1

Rewrite the equation as $- 54 + 16 y i = - 9 x + 8 i$ .

$- 54 + 16 y i = - 9 x + 8 i$

Step 2

Add $54$ to both sides of the equation.

$16 y i = - 9 x + 8 i + 54$

Step 3

Divide each term in $16 y i = - 9 x + 8 i + 54$ by $16 i$ and simplify.

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Step 3.1

Divide each term in $16 y i = - 9 x + 8 i + 54$ by $16 i$ .

$\frac{16 y i}{16 i} = \frac{- 9 x}{16 i} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $16$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{16 y i}{16 i} = \frac{- 9 x}{16 i} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.2.1.2

Rewrite the expression.

$\frac{y i}{i} = \frac{- 9 x}{16 i} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.2.2

Cancel the common factor of $i$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{y i}{i} = \frac{- 9 x}{16 i} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 9 x}{16 i} + \frac{8 i}{16 i} + \frac{54}{16 i}$

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

Multiply the numerator and denominator of $\frac{- 9 x}{16 i}$ by the conjugate of $16 i$ to make the denominator real.

$y = \frac{- 9 x}{16 i} \cdot \frac{i}{i} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.2

Multiply.

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Step 3.3.1.2.1

Combine.

$y = \frac{- 9 x i}{16 i i} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.2.2

Simplify the denominator.

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Step 3.3.1.2.2.1

Add parentheses.

$y = \frac{- 9 x i}{16 (i i)} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.2.2.2

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

$y = \frac{- 9 x i}{16 (i^{1} i)} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.2.2.3

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

$y = \frac{- 9 x i}{16 (i^{1} i^{1})} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.2.2.4

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

$y = \frac{- 9 x i}{16 i^{1 + 1}} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.2.2.5

Add $1$ and $1$ .

$y = \frac{- 9 x i}{16 i^{2}} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.2.2.6

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

$y = \frac{- 9 x i}{16 \cdot - 1} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.3

Multiply $16$ by $- 1$ .

$y = \frac{- 9 x i}{- 16} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.4

Dividing two negative values results in a positive value.

$y = \frac{9 x i}{16} + \frac{8 i}{16 i} + \frac{54}{16 i}$

Step 3.3.1.5

Cancel the common factor of $8$ and $16$ .

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Step 3.3.1.5.1

Factor $8$ out of $8 i$ .

$y = \frac{9 x i}{16} + \frac{8 (i)}{16 i} + \frac{54}{16 i}$

Step 3.3.1.5.2

Cancel the common factors.

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Step 3.3.1.5.2.1

Factor $8$ out of $16 i$ .

$y = \frac{9 x i}{16} + \frac{8 (i)}{8 (2 i)} + \frac{54}{16 i}$

Step 3.3.1.5.2.2

Cancel the common factor.

$y = \frac{9 x i}{16} + \frac{8 i}{8 (2 i)} + \frac{54}{16 i}$

Step 3.3.1.5.2.3

Rewrite the expression.

$y = \frac{9 x i}{16} + \frac{i}{2 i} + \frac{54}{16 i}$

Step 3.3.1.6

Cancel the common factor of $i$ .

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Step 3.3.1.6.1

Cancel the common factor.

$y = \frac{9 x i}{16} + \frac{i}{2 i} + \frac{54}{16 i}$

Step 3.3.1.6.2

Rewrite the expression.

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{54}{16 i}$

Step 3.3.1.7

Cancel the common factor of $54$ and $16$ .

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Step 3.3.1.7.1

Factor $2$ out of $54$ .

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{2 (27)}{16 i}$

Step 3.3.1.7.2

Cancel the common factors.

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Step 3.3.1.7.2.1

Factor $2$ out of $16 i$ .

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{2 (27)}{2 (8 i)}$

Step 3.3.1.7.2.2

Cancel the common factor.

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{2 \cdot 27}{2 (8 i)}$

Step 3.3.1.7.2.3

Rewrite the expression.

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27}{8 i}$

Step 3.3.1.8

Multiply the numerator and denominator of $\frac{27}{8 i}$ by the conjugate of $8 i$ to make the denominator real.

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27}{8 i} \cdot \frac{i}{i}$

Step 3.3.1.9

Multiply.

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Step 3.3.1.9.1

Combine.

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{8 i i}$

Step 3.3.1.9.2

Simplify the denominator.

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Step 3.3.1.9.2.1

Add parentheses.

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{8 (i i)}$

Step 3.3.1.9.2.2

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

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{8 (i^{1} i)}$

Step 3.3.1.9.2.3

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

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{8 (i^{1} i^{1})}$

Step 3.3.1.9.2.4

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

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{8 i^{1 + 1}}$

Step 3.3.1.9.2.5

Add $1$ and $1$ .

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{8 i^{2}}$

Step 3.3.1.9.2.6

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

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{8 \cdot - 1}$

Step 3.3.1.10

Multiply $8$ by $- 1$ .

$y = \frac{9 x i}{16} + \frac{1}{2} + \frac{27 i}{- 8}$

Step 3.3.1.11

Move the negative in front of the fraction.

$y = \frac{9 x i}{16} + \frac{1}{2} - \frac{27 i}{8}$