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.

$\frac{9}{2} \cdot \frac{2 F}{9} + \frac{9}{2} \cdot \frac{2 G}{9} = \frac{9}{2} D$

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 F}{9} + \frac{9}{2} \cdot \frac{2 G}{9} = \frac{9}{2} D$

Rewrite the expression.

$\frac{1}{2} (2 F) + \frac{9}{2} \cdot \frac{2 G}{9} = \frac{9}{2} D$

Cancel the common factor of $2$ .

Factor $2$ out of $2 F$ .

$\frac{1}{2} (2 (F)) + \frac{9}{2} \cdot \frac{2 G}{9} = \frac{9}{2} D$

Cancel the common factor.

$\frac{1}{2} (2 F) + \frac{9}{2} \cdot \frac{2 G}{9} = \frac{9}{2} D$

Rewrite the expression.

$F + \frac{9}{2} \cdot \frac{2 G}{9} = \frac{9}{2} D$

Cancel the common factor of $9$ .

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.

$G = \frac{9 D}{2} - F$

Solve for G D=2/9(F+G)

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