Finite Math Examples

$c = \frac{9}{4} \cdot (k - 78)$

Step 1

Rewrite the equation as $\frac{9}{4} \cdot (k - 78) = c$ .

$\frac{9}{4} \cdot (k - 78) = c$

Step 2

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} (\frac{9}{4} \cdot (k - 78)) = \frac{4}{9} c$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{4}{9} (\frac{9}{4} \cdot (k - 78))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{4}{9} (\frac{9}{4} k + \frac{9}{4} \cdot - 78) = \frac{4}{9} c$

Step 3.1.1.2

Combine $\frac{9}{4}$ and $k$ .

$\frac{4}{9} (\frac{9 k}{4} + \frac{9}{4} \cdot - 78) = \frac{4}{9} c$

Step 3.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.1

Factor $2$ out of $4$ .

$\frac{4}{9} (\frac{9 k}{4} + \frac{9}{2 (2)} \cdot - 78) = \frac{4}{9} c$

Step 3.1.1.3.2

Factor $2$ out of $- 78$ .

$\frac{4}{9} (\frac{9 k}{4} + \frac{9}{2 \cdot 2} \cdot (2 \cdot - 39)) = \frac{4}{9} c$

Step 3.1.1.3.3

Cancel the common factor.

$\frac{4}{9} (\frac{9 k}{4} + \frac{9}{2 \cdot 2} \cdot (2 \cdot - 39)) = \frac{4}{9} c$

Step 3.1.1.3.4

Rewrite the expression.

$\frac{4}{9} (\frac{9 k}{4} + \frac{9}{2} \cdot - 39) = \frac{4}{9} c$

Step 3.1.1.4

Combine $\frac{9}{2}$ and $- 39$ .

$\frac{4}{9} (\frac{9 k}{4} + \frac{9 \cdot - 39}{2}) = \frac{4}{9} c$

Step 3.1.1.5

Simplify the expression.

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Step 3.1.1.5.1

Multiply $9$ by $- 39$ .

$\frac{4}{9} (\frac{9 k}{4} + \frac{- 351}{2}) = \frac{4}{9} c$

Step 3.1.1.5.2

Move the negative in front of the fraction.

$\frac{4}{9} (\frac{9 k}{4} - \frac{351}{2}) = \frac{4}{9} c$

Step 3.1.1.6

Apply the distributive property.

$\frac{4}{9} \cdot \frac{9 k}{4} + \frac{4}{9} (- \frac{351}{2}) = \frac{4}{9} c$

Step 3.1.1.7

Cancel the common factor of $4$ .

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Step 3.1.1.7.1

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 k}{4} + \frac{4}{9} (- \frac{351}{2}) = \frac{4}{9} c$

Step 3.1.1.7.2

Rewrite the expression.

$\frac{1}{9} (9 k) + \frac{4}{9} (- \frac{351}{2}) = \frac{4}{9} c$

Step 3.1.1.8

Cancel the common factor of $9$ .

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Step 3.1.1.8.1

Factor $9$ out of $9 k$ .

$\frac{1}{9} (9 (k)) + \frac{4}{9} (- \frac{351}{2}) = \frac{4}{9} c$

Step 3.1.1.8.2

Cancel the common factor.

$\frac{1}{9} (9 k) + \frac{4}{9} (- \frac{351}{2}) = \frac{4}{9} c$

Step 3.1.1.8.3

Rewrite the expression.

$k + \frac{4}{9} (- \frac{351}{2}) = \frac{4}{9} c$

Step 3.1.1.9

Cancel the common factor of $2$ .

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Step 3.1.1.9.1

Move the leading negative in $- \frac{351}{2}$ into the numerator.

$k + \frac{4}{9} \cdot \frac{- 351}{2} = \frac{4}{9} c$

Step 3.1.1.9.2

Factor $2$ out of $4$ .

$k + \frac{2 (2)}{9} \cdot \frac{- 351}{2} = \frac{4}{9} c$

Step 3.1.1.9.3

Cancel the common factor.

$k + \frac{2 \cdot 2}{9} \cdot \frac{- 351}{2} = \frac{4}{9} c$

Step 3.1.1.9.4

Rewrite the expression.

$k + \frac{2}{9} \cdot - 351 = \frac{4}{9} c$

Step 3.1.1.10

Cancel the common factor of $9$ .

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Step 3.1.1.10.1

Factor $9$ out of $- 351$ .

$k + \frac{2}{9} \cdot (9 (- 39)) = \frac{4}{9} c$

Step 3.1.1.10.2

Cancel the common factor.

$k + \frac{2}{9} \cdot (9 \cdot - 39) = \frac{4}{9} c$

Step 3.1.1.10.3

Rewrite the expression.

$k + 2 \cdot - 39 = \frac{4}{9} c$

Step 3.1.1.11

Multiply $2$ by $- 39$ .

$k - 78 = \frac{4}{9} c$

Step 3.2

Simplify the right side.

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Step 3.2.1

Combine $\frac{4}{9}$ and $c$ .

$k - 78 = \frac{4 c}{9}$

Step 4

Add $78$ to both sides of the equation.

$k = \frac{4 c}{9} + 78$