Algebra Examples

$7 s + 4 m + 2 i = 24$ $5 s + 3 m + 6 i = 30$ $3 s + 7 m + 10 i = 46$

Step 1

Solve for $s$ in $7 s + 4 m + 2 i = 24$ .

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Step 1.1

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

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Step 1.1.1

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

$7 s + 2 i = 24 - 4 m$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

Step 1.1.2

Subtract $2 i$ from both sides of the equation.

$7 s = 24 - 4 m - 2 i$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

$7 s = 24 - 4 m - 2 i$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

Step 1.2

Divide each term in $7 s = 24 - 4 m - 2 i$ by $7$ and simplify.

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Step 1.2.1

Divide each term in $7 s = 24 - 4 m - 2 i$ by $7$ .

$\frac{7 s}{7} = \frac{24}{7} + \frac{- 4 m}{7} + \frac{- 2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $7$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{7 s}{7} = \frac{24}{7} + \frac{- 4 m}{7} + \frac{- 2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

Step 1.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{24}{7} + \frac{- 4 m}{7} + \frac{- 2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

$s = \frac{24}{7} + \frac{- 4 m}{7} + \frac{- 2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

$s = \frac{24}{7} + \frac{- 4 m}{7} + \frac{- 2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$s = \frac{24}{7} - \frac{4 m}{7} + \frac{- 2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$5 s + 3 m + 6 i = 30$

$3 s + 7 m + 10 i = 46$

Step 2

Replace all occurrences of $s$ with $\frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$ in each equation.

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Step 2.1

Replace all occurrences of $s$ in $5 s + 3 m + 6 i = 30$ with $\frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$ .

$5 (\frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $5 (\frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}) + 3 m + 6 i$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$5 (\frac{24}{7}) + 5 (- \frac{4 m}{7}) + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $5 (\frac{24}{7})$ .

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Step 2.2.1.1.2.1.1

Combine $5$ and $\frac{24}{7}$ .

$\frac{5 \cdot 24}{7} + 5 (- \frac{4 m}{7}) + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2.1.2

Multiply $5$ by $24$ .

$\frac{120}{7} + 5 (- \frac{4 m}{7}) + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{120}{7} + 5 (- \frac{4 m}{7}) + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2.2

Multiply $5 (- \frac{4 m}{7})$ .

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Step 2.2.1.1.2.2.1

Multiply $- 1$ by $5$ .

$\frac{120}{7} - 5 \frac{4 m}{7} + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2.2.2

Combine $- 5$ and $\frac{4 m}{7}$ .

$\frac{120}{7} + \frac{- 5 (4 m)}{7} + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2.2.3

Multiply $4$ by $- 5$ .

$\frac{120}{7} + \frac{- 20 m}{7} + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{120}{7} + \frac{- 20 m}{7} + 5 (- \frac{2 i}{7}) + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2.3

Multiply $5 (- \frac{2 i}{7})$ .

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Step 2.2.1.1.2.3.1

Multiply $- 1$ by $5$ .

$\frac{120}{7} + \frac{- 20 m}{7} - 5 \frac{2 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2.3.2

Combine $- 5$ and $\frac{2 i}{7}$ .

$\frac{120}{7} + \frac{- 20 m}{7} + \frac{- 5 (2 i)}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.2.3.3

Multiply $2$ by $- 5$ .

$\frac{120}{7} + \frac{- 20 m}{7} + \frac{- 10 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{120}{7} + \frac{- 20 m}{7} + \frac{- 10 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{120}{7} + \frac{- 20 m}{7} + \frac{- 10 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.3

Simplify each term.

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Step 2.2.1.1.3.1

Move the negative in front of the fraction.

$\frac{120}{7} - \frac{20 m}{7} + \frac{- 10 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.1.3.2

Move the negative in front of the fraction.

$\frac{120}{7} - \frac{20 m}{7} - \frac{10 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{120}{7} - \frac{20 m}{7} - \frac{10 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{120}{7} - \frac{20 m}{7} - \frac{10 i}{7} + 3 m + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.2

To write $3 m$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{120}{7} - \frac{20 m}{7} + 3 m \cdot \frac{7}{7} - \frac{10 i}{7} + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.3

Combine $3 m$ and $\frac{7}{7}$ .

$\frac{120}{7} - \frac{20 m}{7} + \frac{3 m \cdot 7}{7} - \frac{10 i}{7} + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{120}{7} + \frac{- 20 m + 3 m \cdot 7}{7} - \frac{10 i}{7} + 6 i = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.5

Combine the numerators over the common denominator.

$6 i + \frac{120 - 20 m + 3 m \cdot 7 - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.6

Multiply $7$ by $3$ .

$6 i + \frac{120 - 20 m + 21 m - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.7

Add $- 20 m$ and $21 m$ .

$6 i + \frac{120 + m - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.8

Reorder terms.

$6 i + \frac{m + 120 - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.9

To write $6 i$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$6 i \cdot \frac{7}{7} + \frac{m + 120 - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.10

Simplify terms.

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Step 2.2.1.10.1

Combine $6 i$ and $\frac{7}{7}$ .

$\frac{6 i \cdot 7}{7} + \frac{m + 120 - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.10.2

Combine the numerators over the common denominator.

$\frac{6 i \cdot 7 + m + 120 - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{6 i \cdot 7 + m + 120 - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.11

Simplify the numerator.

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Step 2.2.1.11.1

Multiply $7$ by $6$ .

$\frac{42 i + m + 120 - 10 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.2.1.11.2

Subtract $10 i$ from $42 i$ .

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$3 s + 7 m + 10 i = 46$

Step 2.3

Replace all occurrences of $s$ in $3 s + 7 m + 10 i = 46$ with $\frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$ .

$3 (\frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $3 (\frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}) + 7 m + 10 i$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

$3 (\frac{24}{7}) + 3 (- \frac{4 m}{7}) + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $3 (\frac{24}{7})$ .

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Step 2.4.1.1.2.1.1

Combine $3$ and $\frac{24}{7}$ .

$\frac{3 \cdot 24}{7} + 3 (- \frac{4 m}{7}) + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2.1.2

Multiply $3$ by $24$ .

$\frac{72}{7} + 3 (- \frac{4 m}{7}) + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{72}{7} + 3 (- \frac{4 m}{7}) + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2.2

Multiply $3 (- \frac{4 m}{7})$ .

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Step 2.4.1.1.2.2.1

Multiply $- 1$ by $3$ .

$\frac{72}{7} - 3 \frac{4 m}{7} + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2.2.2

Combine $- 3$ and $\frac{4 m}{7}$ .

$\frac{72}{7} + \frac{- 3 (4 m)}{7} + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2.2.3

Multiply $4$ by $- 3$ .

$\frac{72}{7} + \frac{- 12 m}{7} + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{72}{7} + \frac{- 12 m}{7} + 3 (- \frac{2 i}{7}) + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2.3

Multiply $3 (- \frac{2 i}{7})$ .

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Step 2.4.1.1.2.3.1

Multiply $- 1$ by $3$ .

$\frac{72}{7} + \frac{- 12 m}{7} - 3 \frac{2 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2.3.2

Combine $- 3$ and $\frac{2 i}{7}$ .

$\frac{72}{7} + \frac{- 12 m}{7} + \frac{- 3 (2 i)}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.2.3.3

Multiply $2$ by $- 3$ .

$\frac{72}{7} + \frac{- 12 m}{7} + \frac{- 6 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{72}{7} + \frac{- 12 m}{7} + \frac{- 6 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{72}{7} + \frac{- 12 m}{7} + \frac{- 6 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.3

Simplify each term.

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Step 2.4.1.1.3.1

Move the negative in front of the fraction.

$\frac{72}{7} - \frac{12 m}{7} + \frac{- 6 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.1.3.2

Move the negative in front of the fraction.

$\frac{72}{7} - \frac{12 m}{7} - \frac{6 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{72}{7} - \frac{12 m}{7} - \frac{6 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{72}{7} - \frac{12 m}{7} - \frac{6 i}{7} + 7 m + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.2

To write $7 m$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{72}{7} - \frac{12 m}{7} + 7 m \cdot \frac{7}{7} - \frac{6 i}{7} + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.3

Combine $7 m$ and $\frac{7}{7}$ .

$\frac{72}{7} - \frac{12 m}{7} + \frac{7 m \cdot 7}{7} - \frac{6 i}{7} + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.4

Combine the numerators over the common denominator.

$\frac{72}{7} + \frac{- 12 m + 7 m \cdot 7}{7} - \frac{6 i}{7} + 10 i = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.5

Combine the numerators over the common denominator.

$10 i + \frac{72 - 12 m + 7 m \cdot 7 - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.6

Multiply $7$ by $7$ .

$10 i + \frac{72 - 12 m + 49 m - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.7

Add $- 12 m$ and $49 m$ .

$10 i + \frac{72 + 37 m - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.8

Reorder terms.

$10 i + \frac{37 m + 72 - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.9

To write $10 i$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$10 i \cdot \frac{7}{7} + \frac{37 m + 72 - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.10

Simplify terms.

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Step 2.4.1.10.1

Combine $10 i$ and $\frac{7}{7}$ .

$\frac{10 i \cdot 7}{7} + \frac{37 m + 72 - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.10.2

Combine the numerators over the common denominator.

$\frac{10 i \cdot 7 + 37 m + 72 - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{10 i \cdot 7 + 37 m + 72 - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.11

Simplify the numerator.

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Step 2.4.1.11.1

Multiply $7$ by $10$ .

$\frac{70 i + 37 m + 72 - 6 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 2.4.1.11.2

Subtract $6 i$ from $70 i$ .

$\frac{37 m + 72 + 64 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{37 m + 72 + 64 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{37 m + 72 + 64 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{37 m + 72 + 64 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{37 m + 72 + 64 i}{7} = 46$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3

Solve for $m$ in $\frac{37 m + 72 + 64 i}{7} = 46$ .

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Step 3.1

Multiply both sides by $7$ .

$\frac{37 m + 72 + 64 i}{7} \cdot 7 = 46 \cdot 7$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $7$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{37 m + 72 + 64 i}{7} \cdot 7 = 46 \cdot 7$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.2.1.1.2

Rewrite the expression.

$37 m + 72 + 64 i = 46 \cdot 7$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$37 m + 72 + 64 i = 46 \cdot 7$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$37 m + 72 + 64 i = 46 \cdot 7$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $46$ by $7$ .

$37 m + 72 + 64 i = 322$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$37 m + 72 + 64 i = 322$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$37 m + 72 + 64 i = 322$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.3

Solve for $m$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $72$ from both sides of the equation.

$37 m + 64 i = 322 - 72$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.3.1.2

Subtract $64 i$ from both sides of the equation.

$37 m = 322 - 72 - 64 i$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.3.1.3

Subtract $72$ from $322$ .

$37 m = 250 - 64 i$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$37 m = 250 - 64 i$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.3.2

Divide each term in $37 m = 250 - 64 i$ by $37$ and simplify.

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Step 3.3.2.1

Divide each term in $37 m = 250 - 64 i$ by $37$ .

$\frac{37 m}{37} = \frac{250}{37} + \frac{- 64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $37$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{37 m}{37} = \frac{250}{37} + \frac{- 64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.3.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{250}{37} + \frac{- 64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$m = \frac{250}{37} + \frac{- 64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$m = \frac{250}{37} + \frac{- 64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Move the negative in front of the fraction.

$m = \frac{250}{37} - \frac{64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$m = \frac{250}{37} - \frac{64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$m = \frac{250}{37} - \frac{64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$m = \frac{250}{37} - \frac{64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$m = \frac{250}{37} - \frac{64 i}{37}$

$\frac{m + 120 + 32 i}{7} = 30$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4

Replace all occurrences of $m$ with $\frac{250}{37} - \frac{64 i}{37}$ in each equation.

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Step 4.1

Replace all occurrences of $m$ in $\frac{m + 120 + 32 i}{7} = 30$ with $\frac{250}{37} - \frac{64 i}{37}$ .

$\frac{(\frac{250}{37} - \frac{64 i}{37}) + 120 + 32 i}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $\frac{(\frac{250}{37} - \frac{64 i}{37}) + 120 + 32 i}{7}$ .

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Step 4.2.1.1

Simplify the numerator.

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Step 4.2.1.1.1

To write $120$ as a fraction with a common denominator, multiply by $\frac{37}{37}$ .

$\frac{\frac{250}{37} + 120 \cdot \frac{37}{37} - \frac{64 i}{37} + 32 i}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.2

Combine $120$ and $\frac{37}{37}$ .

$\frac{\frac{250}{37} + \frac{120 \cdot 37}{37} - \frac{64 i}{37} + 32 i}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.3

Combine the numerators over the common denominator.

$\frac{\frac{250 + 120 \cdot 37}{37} - \frac{64 i}{37} + 32 i}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.4

Simplify the numerator.

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Step 4.2.1.1.4.1

Multiply $120$ by $37$ .

$\frac{\frac{250 + 4440}{37} - \frac{64 i}{37} + 32 i}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.4.2

Add $250$ and $4440$ .

$\frac{\frac{4690}{37} - \frac{64 i}{37} + 32 i}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{\frac{4690}{37} - \frac{64 i}{37} + 32 i}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.5

To write $32 i$ as a fraction with a common denominator, multiply by $\frac{37}{37}$ .

$\frac{\frac{4690}{37} - \frac{64 i}{37} + 32 i \cdot \frac{37}{37}}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.6

Combine $32 i$ and $\frac{37}{37}$ .

$\frac{\frac{4690}{37} - \frac{64 i}{37} + \frac{32 i \cdot 37}{37}}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.7

Combine the numerators over the common denominator.

$\frac{\frac{4690}{37} + \frac{1120 i}{37}}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.1.8

Combine the numerators over the common denominator.

$\frac{\frac{4690 + 1120 i}{37}}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{\frac{4690 + 1120 i}{37}}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{4690 + 1120 i}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.3

Split the fraction $\frac{4690 + 1120 i}{37}$ into two fractions.

$(\frac{4690}{37} + \frac{1120 i}{37}) (\frac{1}{7}) = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.4

Apply the distributive property.

$\frac{4690}{37} \cdot \frac{1}{7} + \frac{1120 i}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.5

Cancel the common factor of $7$ .

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Step 4.2.1.5.1

Factor $7$ out of $4690$ .

$\frac{7 (670)}{37} \cdot \frac{1}{7} + \frac{1120 i}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.5.2

Cancel the common factor.

$\frac{7 \cdot 670}{37} \cdot \frac{1}{7} + \frac{1120 i}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.5.3

Rewrite the expression.

$\frac{670}{37} + \frac{1120 i}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{670}{37} + \frac{1120 i}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.6

Cancel the common factor of $7$ .

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Step 4.2.1.6.1

Factor $7$ out of $1120 i$ .

$\frac{670}{37} + \frac{7 (160 i)}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.6.2

Cancel the common factor.

$\frac{670}{37} + \frac{7 (160 i)}{37} \cdot \frac{1}{7} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.2.1.6.3

Rewrite the expression.

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$

Step 4.3

Replace all occurrences of $m$ in $s = \frac{24}{7} - \frac{4 m}{7} - \frac{2 i}{7}$ with $\frac{250}{37} - \frac{64 i}{37}$ .

$s = \frac{24}{7} - \frac{4 (\frac{250}{37} - \frac{64 i}{37})}{7} - \frac{2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $\frac{24}{7} - \frac{4 (\frac{250}{37} - \frac{64 i}{37})}{7} - \frac{2 i}{7}$ .

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Step 4.4.1.1

Combine the numerators over the common denominator.

$s = \frac{24 - 4 (\frac{250}{37} - \frac{64 i}{37}) - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.2

Simplify each term.

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Step 4.4.1.2.1

Apply the distributive property.

$s = \frac{24 - 4 (\frac{250}{37}) - 4 (- \frac{64 i}{37}) - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.2.2

Multiply $- 4 (\frac{250}{37})$ .

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Step 4.4.1.2.2.1

Combine $- 4$ and $\frac{250}{37}$ .

$s = \frac{24 + \frac{- 4 \cdot 250}{37} - 4 (- \frac{64 i}{37}) - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.2.2.2

Multiply $- 4$ by $250$ .

$s = \frac{24 + \frac{- 1000}{37} - 4 (- \frac{64 i}{37}) - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24 + \frac{- 1000}{37} - 4 (- \frac{64 i}{37}) - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.2.3

Multiply $- 4 (- \frac{64 i}{37})$ .

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Step 4.4.1.2.3.1

Multiply $- 1$ by $- 4$ .

$s = \frac{24 + \frac{- 1000}{37} + 4 (\frac{64 i}{37}) - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.2.3.2

Combine $4$ and $\frac{64 i}{37}$ .

$s = \frac{24 + \frac{- 1000}{37} + \frac{4 (64 i)}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.2.3.3

Multiply $64$ by $4$ .

$s = \frac{24 + \frac{- 1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24 + \frac{- 1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.2.4

Move the negative in front of the fraction.

$s = \frac{24 - \frac{1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{24 - \frac{1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.3

To write $24$ as a fraction with a common denominator, multiply by $\frac{37}{37}$ .

$s = \frac{24 \cdot \frac{37}{37} - \frac{1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.4

Combine $24$ and $\frac{37}{37}$ .

$s = \frac{\frac{24 \cdot 37}{37} - \frac{1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.5

Combine the numerators over the common denominator.

$s = \frac{\frac{24 \cdot 37 - 1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.6

Simplify the numerator.

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Step 4.4.1.6.1

Multiply $24$ by $37$ .

$s = \frac{\frac{888 - 1000}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.6.2

Subtract $1000$ from $888$ .

$s = \frac{\frac{- 112}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{\frac{- 112}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.7

Move the negative in front of the fraction.

$s = \frac{- \frac{112}{37} + \frac{256 i}{37} - 2 i}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.8

To write $- 2 i$ as a fraction with a common denominator, multiply by $\frac{37}{37}$ .

$s = \frac{- \frac{112}{37} + \frac{256 i}{37} - 2 i \cdot \frac{37}{37}}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.9

Combine $- 2 i$ and $\frac{37}{37}$ .

$s = \frac{- \frac{112}{37} + \frac{256 i}{37} + \frac{- 2 i \cdot 37}{37}}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.10

Combine fractions.

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Step 4.4.1.10.1

Combine the numerators over the common denominator.

$s = \frac{- \frac{112}{37} + \frac{182 i}{37}}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.10.2

Combine the numerators over the common denominator.

$s = \frac{\frac{- 112 + 182 i}{37}}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{\frac{- 112 + 182 i}{37}}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.11

Multiply the numerator by the reciprocal of the denominator.

$s = \frac{- 112 + 182 i}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.12

Split the fraction $\frac{- 112 + 182 i}{37}$ into two fractions.

$s = (\frac{- 112}{37} + \frac{182 i}{37}) (\frac{1}{7})$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.13

Move the negative in front of the fraction.

$s = (- \frac{112}{37} + \frac{182 i}{37}) (\frac{1}{7})$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.14

Apply the distributive property.

$s = - \frac{112}{37} \cdot \frac{1}{7} + \frac{182 i}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.15

Cancel the common factor of $7$ .

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Step 4.4.1.15.1

Move the leading negative in $- \frac{112}{37}$ into the numerator.

$s = \frac{- 112}{37} \cdot \frac{1}{7} + \frac{182 i}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.15.2

Factor $7$ out of $- 112$ .

$s = \frac{7 (- 16)}{37} \cdot \frac{1}{7} + \frac{182 i}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.15.3

Cancel the common factor.

$s = \frac{7 \cdot - 16}{37} \cdot \frac{1}{7} + \frac{182 i}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.15.4

Rewrite the expression.

$s = \frac{- 16}{37} + \frac{182 i}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{- 16}{37} + \frac{182 i}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.16

Cancel the common factor of $7$ .

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Step 4.4.1.16.1

Factor $7$ out of $182 i$ .

$s = \frac{- 16}{37} + \frac{7 (26 i)}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.16.2

Cancel the common factor.

$s = \frac{- 16}{37} + \frac{7 (26 i)}{37} \cdot \frac{1}{7}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.16.3

Rewrite the expression.

$s = \frac{- 16}{37} + \frac{26 i}{37}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = \frac{- 16}{37} + \frac{26 i}{37}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 4.4.1.17

Move the negative in front of the fraction.

$s = - \frac{16}{37} + \frac{26 i}{37}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = - \frac{16}{37} + \frac{26 i}{37}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = - \frac{16}{37} + \frac{26 i}{37}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

$s = - \frac{16}{37} + \frac{26 i}{37}$

$\frac{670}{37} + \frac{160 i}{37} = 30$

$m = \frac{250}{37} - \frac{64 i}{37}$

Step 5

Since $\frac{670}{37} + \frac{160 i}{37} = 30$ is not true, there is no solution.

No solution