Algebra Examples

$F (c) = \frac{9}{5} c + 32$

Step 1

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

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

Step 2

Subtract $\frac{9 c}{5}$ from both sides of the equation.

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

Step 3

Factor $c$ out of $F c - \frac{9 c}{5}$ .

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Step 3.1

Factor $c$ out of $F c$ .

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

Step 3.2

Factor $c$ out of $- \frac{9 c}{5}$ .

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

Step 3.3

Factor $c$ out of $c F + c (- \frac{9}{5})$ .

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

Step 4

Divide each term in $c (F - \frac{9}{5}) = 32$ by $F - \frac{9}{5}$ and simplify.

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Step 4.1

Divide each term in $c (F - \frac{9}{5}) = 32$ by $F - \frac{9}{5}$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $F - \frac{9}{5}$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $c$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify the denominator.

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Step 4.3.1.1

To write $F$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4.3.1.2

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

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

Step 4.3.1.3

Combine the numerators over the common denominator.

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

Step 4.3.1.4

Move $5$ to the left of $F$ .

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

Step 4.3.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 4.3.3

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

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Step 4.3.3.1

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

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

Step 4.3.3.2

Multiply $32$ by $5$ .

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