Solve for f D=4/7(f+g)

$D = \frac{4}{7} (f + g)$

Step 1

Rewrite the equation as $\frac{4}{7} \cdot (f + g) = D$ .

$\frac{4}{7} \cdot (f + g) = D$

Step 2

Multiply both sides of the equation by $\frac{7}{4}$ .

$\frac{7}{4} (\frac{4}{7} \cdot (f + g)) = \frac{7}{4} D$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{7}{4} (\frac{4}{7} \cdot (f + g))$ .

Apply the distributive property.

$\frac{7}{4} (\frac{4}{7} f + \frac{4}{7} g) = \frac{7}{4} D$

Combine $\frac{4}{7}$ and $f$ .

$\frac{7}{4} (\frac{4 f}{7} + \frac{4}{7} g) = \frac{7}{4} D$

Combine $\frac{4}{7}$ and $g$ .

$\frac{7}{4} (\frac{4 f}{7} + \frac{4 g}{7}) = \frac{7}{4} D$

Apply the distributive property.

$\frac{7}{4} \cdot \frac{4 f}{7} + \frac{7}{4} \cdot \frac{4 g}{7} = \frac{7}{4} D$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7}{4} \cdot \frac{4 f}{7} + \frac{7}{4} \cdot \frac{4 g}{7} = \frac{7}{4} D$

Rewrite the expression.

$\frac{1}{4} (4 f) + \frac{7}{4} \cdot \frac{4 g}{7} = \frac{7}{4} D$

Cancel the common factor of $4$ .

Factor $4$ out of $4 f$ .

$\frac{1}{4} (4 (f)) + \frac{7}{4} \cdot \frac{4 g}{7} = \frac{7}{4} D$

Cancel the common factor.

$\frac{1}{4} (4 f) + \frac{7}{4} \cdot \frac{4 g}{7} = \frac{7}{4} D$

Rewrite the expression.

$f + \frac{7}{4} \cdot \frac{4 g}{7} = \frac{7}{4} D$

Cancel the common factor of $7$ .

Cancel the common factor.

$f + \frac{7}{4} \cdot \frac{4 g}{7} = \frac{7}{4} D$

Rewrite the expression.

$f + \frac{1}{4} (4 g) = \frac{7}{4} D$

Cancel the common factor of $4$ .

Factor $4$ out of $4 g$ .

$f + \frac{1}{4} (4 (g)) = \frac{7}{4} D$

Cancel the common factor.

$f + \frac{1}{4} (4 g) = \frac{7}{4} D$

Rewrite the expression.

$f + g = \frac{7}{4} D$

Simplify the right side.

Combine $\frac{7}{4}$ and $D$ .

$f + g = \frac{7 D}{4}$

Step 4

Subtract $g$ from both sides of the equation.

$f = \frac{7 D}{4} - g$

Solve for f D=4/7(f+g)

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