Solve for f D=2/3(f+g)

$D = \frac{2}{3} (f + g)$

Step 1

Rewrite the equation as $\frac{2}{3} \cdot (f + g) = D$ .

$\frac{2}{3} \cdot (f + g) = D$

Step 2

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (f + g)) = \frac{3}{2} D$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (f + g))$ .

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} f + \frac{2}{3} g) = \frac{3}{2} D$

Combine $\frac{2}{3}$ and $f$ .

$\frac{3}{2} (\frac{2 f}{3} + \frac{2}{3} g) = \frac{3}{2} D$

Combine $\frac{2}{3}$ and $g$ .

$\frac{3}{2} (\frac{2 f}{3} + \frac{2 g}{3}) = \frac{3}{2} D$

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 f}{3} + \frac{3}{2} \cdot \frac{2 g}{3} = \frac{3}{2} D$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 f}{3} + \frac{3}{2} \cdot \frac{2 g}{3} = \frac{3}{2} D$

Rewrite the expression.

$\frac{1}{2} (2 f) + \frac{3}{2} \cdot \frac{2 g}{3} = \frac{3}{2} D$

Cancel the common factor of $2$ .

Factor $2$ out of $2 f$ .

$\frac{1}{2} (2 (f)) + \frac{3}{2} \cdot \frac{2 g}{3} = \frac{3}{2} D$

Cancel the common factor.

$\frac{1}{2} (2 f) + \frac{3}{2} \cdot \frac{2 g}{3} = \frac{3}{2} D$

Rewrite the expression.

$f + \frac{3}{2} \cdot \frac{2 g}{3} = \frac{3}{2} D$

Cancel the common factor of $3$ .

Cancel the common factor.

$f + \frac{3}{2} \cdot \frac{2 g}{3} = \frac{3}{2} D$

Rewrite the expression.

$f + \frac{1}{2} (2 g) = \frac{3}{2} D$

Cancel the common factor of $2$ .

Factor $2$ out of $2 g$ .

$f + \frac{1}{2} (2 (g)) = \frac{3}{2} D$

Cancel the common factor.

$f + \frac{1}{2} (2 g) = \frac{3}{2} D$

Rewrite the expression.

$f + g = \frac{3}{2} D$

Simplify the right side.

Combine $\frac{3}{2}$ and $D$ .

$f + g = \frac{3 D}{2}$

Step 4

Subtract $g$ from both sides of the equation.

$f = \frac{3 D}{2} - g$

Solve for f D=2/3(f+g)

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