Solve for f c=5/9(f-32)

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

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.

Simplify the left side.

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

Apply the distributive property.

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

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

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

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

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

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

Multiply $5$ by $- 32$ .

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

Move the negative in front of the fraction.

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

Apply the distributive property.

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

Cancel the common factor of $9$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5} (5 f) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} c$

Cancel the common factor of $5$ .

Factor $5$ out of $5 f$ .

$\frac{1}{5} (5 (f)) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} c$

Cancel the common factor.

$\frac{1}{5} (5 f) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} c$

Rewrite the expression.

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

Cancel the common factor of $9$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$f + \frac{1}{5} \cdot - 160 = \frac{9}{5} c$

Cancel the common factor of $5$ .

Factor $5$ out of $- 160$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

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

Step 4

Add $32$ to both sides of the equation.

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

Solve for f c=5/9(f-32)

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