Solve for g 2/3g=8(3/8g-2)+1/3g

$\frac{2}{3} g = 8 (\frac{3}{8} g - 2) + \frac{1}{3} g$

Since $g$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$8 (\frac{3}{8} g - 2) + \frac{1}{3} g = \frac{2}{3} g$

Simplify $8 (\frac{3}{8} g - 2) + \frac{1}{3} g$ .

Simplify each term.

Combine $\frac{3}{8}$ and $g$ .

$8 (\frac{3 g}{8} - 2) + \frac{1}{3} g = \frac{2}{3} g$

Apply the distributive property.

$8 \frac{3 g}{8} + 8 \cdot - 2 + \frac{1}{3} g = \frac{2}{3} g$

Cancel the common factor of $8$ .

Cancel the common factor.

$8 \frac{3 g}{8} + 8 \cdot - 2 + \frac{1}{3} g = \frac{2}{3} g$

Rewrite the expression.

$3 g + 8 \cdot - 2 + \frac{1}{3} g = \frac{2}{3} g$

Multiply $8$ by $- 2$ .

$3 g - 16 + \frac{1}{3} g = \frac{2}{3} g$

Combine $\frac{1}{3}$ and $g$ .

$3 g - 16 + \frac{g}{3} = \frac{2}{3} g$

To write $3 g$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$3 g \cdot \frac{3}{3} + \frac{g}{3} - 16 = \frac{2}{3} g$

Simplify terms.

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

$\frac{3 g \cdot 3}{3} + \frac{g}{3} - 16 = \frac{2}{3} g$

Combine the numerators over the common denominator.

$\frac{3 g \cdot 3 + g}{3} - 16 = \frac{2}{3} g$

Simplify each term.

Simplify the numerator.

Factor $g$ out of $3 g \cdot 3 + g$ .

Factor $g$ out of $3 g \cdot 3$ .

$\frac{g (3 \cdot 3) + g}{3} - 16 = \frac{2}{3} g$

Raise $g$ to the power of $1$ .

$\frac{g (3 \cdot 3) + g^{1}}{3} - 16 = \frac{2}{3} g$

Factor $g$ out of $g^{1}$ .

$\frac{g (3 \cdot 3) + g \cdot 1}{3} - 16 = \frac{2}{3} g$

Factor $g$ out of $g (3 \cdot 3) + g \cdot 1$ .

$\frac{g (3 \cdot 3 + 1)}{3} - 16 = \frac{2}{3} g$

Multiply $3$ by $3$ .

$\frac{g (9 + 1)}{3} - 16 = \frac{2}{3} g$

Add $9$ and $1$ .

$\frac{g \cdot 10}{3} - 16 = \frac{2}{3} g$

Move $10$ to the left of $g$ .

$\frac{10 g}{3} - 16 = \frac{2}{3} g$

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

$\frac{10 g}{3} - 16 = \frac{2 g}{3}$

Move all terms containing $g$ to the left side of the equation.

Subtract $\frac{2 g}{3}$ from both sides of the equation.

$\frac{10 g}{3} - 16 - \frac{2 g}{3} = 0$

Combine the numerators over the common denominator.

$- 16 + \frac{10 g - 2 g}{3} = 0$

Subtract $2 g$ from $10 g$ .

$- 16 + \frac{8 g}{3} = 0$

Add $16$ to both sides of the equation.

$\frac{8 g}{3} = 16$

Multiply both sides of the equation by $\frac{3}{8}$ .

$\frac{3}{8} \cdot \frac{8 g}{3} = \frac{3}{8} \cdot 16$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{8} \cdot \frac{8 g}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{8} \cdot \frac{8 g}{3} = \frac{3}{8} \cdot 16$

Rewrite the expression.

$\frac{1}{8} (8 g) = \frac{3}{8} \cdot 16$

Cancel the common factor of $8$ .

Factor $8$ out of $8 g$ .

$\frac{1}{8} (8 (g)) = \frac{3}{8} \cdot 16$

Cancel the common factor.

$\frac{1}{8} (8 g) = \frac{3}{8} \cdot 16$

Rewrite the expression.

$g = \frac{3}{8} \cdot 16$

Simplify the right side.

Simplify $\frac{3}{8} \cdot 16$ .

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$g = \frac{3}{8} \cdot (8 (2))$

Cancel the common factor.

$g = \frac{3}{8} \cdot (8 \cdot 2)$

Rewrite the expression.

$g = 3 \cdot 2$

Multiply $3$ by $2$ .

$g = 6$

Solve for g 2/3g=8(3/8g-2)+1/3g

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