Algebra Examples

f = \frac{9}{5} c + 32

$f = \frac{9}{5} c + 32$

Step 1

Rewrite the equation as

\frac{9}{5} c + 32 = f

$\frac{9}{5} c + 32 = f$ .

\frac{9}{5} c + 32 = f

$\frac{9}{5} c + 32 = f$

Step 2

Combine

\frac{9}{5}

$\frac{9}{5}$ and

c

$c$ .

\frac{9 c}{5} + 32 = f

$\frac{9 c}{5} + 32 = f$

Step 3

Subtract

32

$32$ from both sides of the equation.

\frac{9 c}{5} = f - 32

$\frac{9 c}{5} = f - 32$

Step 4

Multiply both sides of the equation by

\frac{5}{9}

$\frac{5}{9}$ .

\frac{5}{9} \cdot \frac{9 c}{5} = \frac{5}{9} (f - 32)

$\frac{5}{9} \cdot \frac{9 c}{5} = \frac{5}{9} (f - 32)$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify

\frac{5}{9} \cdot \frac{9 c}{5}

$\frac{5}{9} \cdot \frac{9 c}{5}$ .

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Step 5.1.1.1

Cancel the common factor of

5

$5$ .

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Step 5.1.1.1.1

Cancel the common factor.

\frac{5}{9} \cdot \frac{9 c}{5} = \frac{5}{9} (f - 32)

$\frac{5}{9} \cdot \frac{9 c}{5} = \frac{5}{9} (f - 32)$

Step 5.1.1.1.2

Rewrite the expression.

\frac{1}{9} (9 c) = \frac{5}{9} (f - 32)

$\frac{1}{9} (9 c) = \frac{5}{9} (f - 32)$

\frac{1}{9} (9 c) = \frac{5}{9} (f - 32)

$\frac{1}{9} (9 c) = \frac{5}{9} (f - 32)$

Step 5.1.1.2

Cancel the common factor of

9

$9$ .

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Step 5.1.1.2.1

Factor

9

$9$ out of

9 c

$9 c$ .

\frac{1}{9} (9 (c)) = \frac{5}{9} (f - 32)

$\frac{1}{9} (9 (c)) = \frac{5}{9} (f - 32)$

Step 5.1.1.2.2

Cancel the common factor.

\frac{1}{9} (9 c) = \frac{5}{9} (f - 32)

$\frac{1}{9} (9 c) = \frac{5}{9} (f - 32)$

Step 5.1.1.2.3

Rewrite the expression.

c = \frac{5}{9} (f - 32)

$c = \frac{5}{9} (f - 32)$

c = \frac{5}{9} (f - 32)

$c = \frac{5}{9} (f - 32)$

c = \frac{5}{9} (f - 32)

$c = \frac{5}{9} (f - 32)$

c = \frac{5}{9} (f - 32)

$c = \frac{5}{9} (f - 32)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

\frac{5}{9} (f - 32)

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

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Step 5.2.1.1

Apply the distributive property.

c = \frac{5}{9} f + \frac{5}{9} \cdot - 32

$c = \frac{5}{9} f + \frac{5}{9} \cdot - 32$

Step 5.2.1.2

Combine

\frac{5}{9}

$\frac{5}{9}$ and

f

$f$ .

c = \frac{5 f}{9} + \frac{5}{9} \cdot - 32

$c = \frac{5 f}{9} + \frac{5}{9} \cdot - 32$

Step 5.2.1.3

Multiply

\frac{5}{9} \cdot - 32

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

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Step 5.2.1.3.1

Combine

\frac{5}{9}

$\frac{5}{9}$ and

- 32

$- 32$ .

c = \frac{5 f}{9} + \frac{5 \cdot - 32}{9}

$c = \frac{5 f}{9} + \frac{5 \cdot - 32}{9}$

Step 5.2.1.3.2

Multiply

5

$5$ by

- 32

$- 32$ .

c = \frac{5 f}{9} + \frac{- 160}{9}

$c = \frac{5 f}{9} + \frac{- 160}{9}$

c = \frac{5 f}{9} + \frac{- 160}{9}

$c = \frac{5 f}{9} + \frac{- 160}{9}$

Step 5.2.1.4

Move the negative in front of the fraction.

c = \frac{5 f}{9} - \frac{160}{9}

$c = \frac{5 f}{9} - \frac{160}{9}$

c = \frac{5 f}{9} - \frac{160}{9}

$c = \frac{5 f}{9} - \frac{160}{9}$

c = \frac{5 f}{9} - \frac{160}{9}

$c = \frac{5 f}{9} - \frac{160}{9}$

c = \frac{5 f}{9} - \frac{160}{9}

$c = \frac{5 f}{9} - \frac{160}{9}$

f = \frac{9}{5} c + 32

$f = \frac{9}{5} c + 32$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$