Solve for F 30=5/9(F-32)

$30 = \frac{5}{9} (F - 32)$

Step 1

Rewrite the equation as $\frac{5}{9} \cdot (F - 32) = 30$ .

$\frac{5}{9} \cdot (F - 32) = 30$

Step 2

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

$\frac{9}{5} (\frac{5}{9} \cdot (F - 32)) = \frac{9}{5} \cdot 30$

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.

$\frac{9}{5} (\frac{5}{9} F + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot 30$

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

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot 30$

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

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

$\frac{9}{5} (\frac{5 F}{9} + \frac{5 \cdot - 32}{9}) = \frac{9}{5} \cdot 30$

Multiply $5$ by $- 32$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{- 160}{9}) = \frac{9}{5} \cdot 30$

Move the negative in front of the fraction.

$\frac{9}{5} (\frac{5 F}{9} - \frac{160}{9}) = \frac{9}{5} \cdot 30$

Apply the distributive property.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 30$

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 30$

Rewrite the expression.

$\frac{1}{5} (5 F) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 30$

Cancel the common factor of $5$ .

Factor $5$ out of $5 F$ .

$\frac{1}{5} (5 (F)) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 30$

Cancel the common factor.

$\frac{1}{5} (5 F) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 30$

Rewrite the expression.

$F + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 30$

Cancel the common factor of $9$ .

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

$F + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot 30$

Cancel the common factor.

$F + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot 30$

Rewrite the expression.

$F + \frac{1}{5} \cdot - 160 = \frac{9}{5} \cdot 30$

Cancel the common factor of $5$ .

Factor $5$ out of $- 160$ .

$F + \frac{1}{5} \cdot (5 (- 32)) = \frac{9}{5} \cdot 30$

Cancel the common factor.

$F + \frac{1}{5} \cdot (5 \cdot - 32) = \frac{9}{5} \cdot 30$

Rewrite the expression.

$F - 32 = \frac{9}{5} \cdot 30$

Simplify the right side.

Simplify $\frac{9}{5} \cdot 30$ .

Cancel the common factor of $5$ .

Factor $5$ out of $30$ .

$F - 32 = \frac{9}{5} \cdot (5 (6))$

Cancel the common factor.

$F - 32 = \frac{9}{5} \cdot (5 \cdot 6)$

Rewrite the expression.

$F - 32 = 9 \cdot 6$

Multiply $9$ by $6$ .

$F - 32 = 54$

Step 4

Move all terms not containing $F$ to the right side of the equation.

Add $32$ to both sides of the equation.

$F = 54 + 32$

Add $54$ and $32$ .

$F = 86$

Solve for F 30=5/9(F-32)

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