Solve for a f=g+1/7ua

$f = g + \frac{1}{7} u a$

Step 1

Rewrite the equation as $g + \frac{1}{7} \cdot (u a) = f$ .

$g + \frac{1}{7} \cdot (u a) = f$

Step 2

Multiply $\frac{1}{7} (u a)$ .

Combine $u$ and $\frac{1}{7}$ .

$g + \frac{u}{7} a = f$

Combine $\frac{u}{7}$ and $a$ .

$g + \frac{u a}{7} = f$

Step 3

Subtract $g$ from both sides of the equation.

$\frac{u a}{7} = f - g$

Step 4

Multiply both sides of the equation by $7$ .

$7 \frac{u a}{7} = 7 (f - g)$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{u a}{7} = 7 (f - g)$

Rewrite the expression.

$u a = 7 (f - g)$

Simplify the right side.

Simplify $7 (f - g)$ .

Apply the distributive property.

$u a = 7 f + 7 (- g)$

Multiply $- 1$ by $7$ .

$u a = 7 f - 7 g$

Step 6

Divide each term in $u a = 7 f - 7 g$ by $u$ and simplify.

Divide each term in $u a = 7 f - 7 g$ by $u$ .

$\frac{u a}{u} = \frac{7 f}{u} + \frac{- 7 g}{u}$

Simplify the left side.

Cancel the common factor of $u$ .

Cancel the common factor.

$\frac{u a}{u} = \frac{7 f}{u} + \frac{- 7 g}{u}$

Divide $a$ by $1$ .

$a = \frac{7 f}{u} + \frac{- 7 g}{u}$

Simplify the right side.

Move the negative in front of the fraction.

$a = \frac{7 f}{u} - \frac{7 g}{u}$