Algebra Examples

$C = \frac{5}{9} (F - 32)$

Step 1

Rewrite the equation as $\frac{5}{9} \cdot (F - 32) = C$ .

$\frac{5}{9} \cdot (F - 32) = C$

Step 2

Multiply both sides of the equation by $\frac{9}{5}$ .

$\frac{9}{5} (\frac{5}{9} \cdot (F - 32)) = \frac{9}{5} C$

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 $\frac{9}{5} (\frac{5}{9} \cdot (F - 32))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{9}{5} (\frac{5}{9} F + \frac{5}{9} \cdot - 32) = \frac{9}{5} C$

Step 3.1.1.2

Combine $\frac{5}{9}$ and $F$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{9} \cdot - 32) = \frac{9}{5} C$

Step 3.1.1.3

Multiply $\frac{5}{9} \cdot - 32$ .

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Step 3.1.1.3.1

Combine $\frac{5}{9}$ and $- 32$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{5 \cdot - 32}{9}) = \frac{9}{5} C$

Step 3.1.1.3.2

Multiply $5$ by $- 32$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{- 160}{9}) = \frac{9}{5} C$

Step 3.1.1.4

Move the negative in front of the fraction.

$\frac{9}{5} (\frac{5 F}{9} - \frac{160}{9}) = \frac{9}{5} C$

Step 3.1.1.5

Apply the distributive property.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} C$

Step 3.1.1.6

Cancel the common factor of $9$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} C$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{5} (5 F) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} C$

Step 3.1.1.7

Cancel the common factor of $5$ .

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Step 3.1.1.7.1

Factor $5$ out of $5 F$ .

$\frac{1}{5} (5 (F)) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} C$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{5} (5 F) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} C$

Step 3.1.1.7.3

Rewrite the expression.

$F + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} C$

Step 3.1.1.8

Cancel the common factor of $9$ .

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Step 3.1.1.8.1

Move the leading negative in $- \frac{160}{9}$ into the numerator.

$F + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} C$

Step 3.1.1.8.2

Cancel the common factor.

$F + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} C$

Step 3.1.1.8.3

Rewrite the expression.

$F + \frac{1}{5} \cdot - 160 = \frac{9}{5} C$

Step 3.1.1.9

Cancel the common factor of $5$ .

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Step 3.1.1.9.1

Factor $5$ out of $- 160$ .

$F + \frac{1}{5} \cdot (5 (- 32)) = \frac{9}{5} C$

Step 3.1.1.9.2

Cancel the common factor.

$F + \frac{1}{5} \cdot (5 \cdot - 32) = \frac{9}{5} C$

Step 3.1.1.9.3

Rewrite the expression.

$F - 32 = \frac{9}{5} C$

Step 3.2

Simplify the right side.

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Step 3.2.1

Combine $\frac{9}{5}$ and $C$ .

$F - 32 = \frac{9 C}{5}$

Step 4

Add $32$ to both sides of the equation.

$F = \frac{9 C}{5} + 32$