Solve for g D=2/9(f-g)

$D = \frac{2}{9} (f - g)$

Step 1

Rewrite the equation as $\frac{2}{9} \cdot (f - g) = D$ .

$\frac{2}{9} \cdot (f - g) = D$

Step 2

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} (\frac{2}{9} \cdot (f - g)) = \frac{9}{2} D$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{9}{2} (\frac{2}{9} \cdot (f - g))$ .

Apply the distributive property.

$\frac{9}{2} (\frac{2}{9} f + \frac{2}{9} (- g)) = \frac{9}{2} D$

Combine $\frac{2}{9}$ and $f$ .

$\frac{9}{2} (\frac{2 f}{9} + \frac{2}{9} (- g)) = \frac{9}{2} D$

Combine $\frac{2}{9}$ and $g$ .

$\frac{9}{2} (\frac{2 f}{9} - \frac{2 g}{9}) = \frac{9}{2} D$

Apply the distributive property.

$\frac{9}{2} \cdot \frac{2 f}{9} + \frac{9}{2} (- \frac{2 g}{9}) = \frac{9}{2} D$

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 f}{9} + \frac{9}{2} (- \frac{2 g}{9}) = \frac{9}{2} D$

Rewrite the expression.

$\frac{1}{2} (2 f) + \frac{9}{2} (- \frac{2 g}{9}) = \frac{9}{2} D$

Cancel the common factor of $2$ .

Factor $2$ out of $2 f$ .

$\frac{1}{2} (2 (f)) + \frac{9}{2} (- \frac{2 g}{9}) = \frac{9}{2} D$

Cancel the common factor.

$\frac{1}{2} (2 f) + \frac{9}{2} (- \frac{2 g}{9}) = \frac{9}{2} D$

Rewrite the expression.

$f + \frac{9}{2} (- \frac{2 g}{9}) = \frac{9}{2} D$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{2 g}{9}$ into the numerator.

$f + \frac{9}{2} \cdot \frac{- 2 g}{9} = \frac{9}{2} D$

Cancel the common factor.

$f + \frac{9}{2} \cdot \frac{- 2 g}{9} = \frac{9}{2} D$

Rewrite the expression.

$f + \frac{1}{2} (- 2 g) = \frac{9}{2} D$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 g$ .

$f + \frac{1}{2} (2 (- g)) = \frac{9}{2} D$

Cancel the common factor.

$f + \frac{1}{2} (2 (- g)) = \frac{9}{2} D$

Rewrite the expression.

$f - g = \frac{9}{2} D$

Simplify the right side.

Combine $\frac{9}{2}$ and $D$ .

$f - g = \frac{9 D}{2}$

Step 4

Subtract $f$ from both sides of the equation.

$- g = \frac{9 D}{2} - f$

Step 5

Divide each term in $- g = \frac{9 D}{2} - f$ by $- 1$ and simplify.

Divide each term in $- g = \frac{9 D}{2} - f$ by $- 1$ .

$\frac{- g}{- 1} = \frac{\frac{9 D}{2}}{- 1} + \frac{- f}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{g}{1} = \frac{\frac{9 D}{2}}{- 1} + \frac{- f}{- 1}$

Divide $g$ by $1$ .

$g = \frac{\frac{9 D}{2}}{- 1} + \frac{- f}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{9 D}{2}}{- 1}$ .

$g = - 1 \cdot \frac{9 D}{2} + \frac{- f}{- 1}$

Rewrite $- 1 \cdot \frac{9 D}{2}$ as $- \frac{9 D}{2}$ .

$g = - \frac{9 D}{2} + \frac{- f}{- 1}$

Dividing two negative values results in a positive value.

$g = - \frac{9 D}{2} + \frac{f}{1}$

Divide $f$ by $1$ .

$g = - \frac{9 D}{2} + f$

Solve for g D=2/9(f-g)

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