Solve for g 5/3g=2g-2/3g+2

$\frac{5}{3} g = 2 g - \frac{2}{3} g + 2$

Step 1

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

$2 g - \frac{2}{3} g + 2 = \frac{5}{3} g$

Step 2

Simplify $2 g - \frac{2}{3} g + 2$ .

Simplify each term.

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

$2 g - \frac{g \cdot 2}{3} + 2 = \frac{5}{3} g$

Move $2$ to the left of $g$ .

$2 g - \frac{2 g}{3} + 2 = \frac{5}{3} g$

To write $2 g$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 g \cdot \frac{3}{3} - \frac{2 g}{3} + 2 = \frac{5}{3} g$

Simplify terms.

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

$\frac{2 g \cdot 3}{3} - \frac{2 g}{3} + 2 = \frac{5}{3} g$

Combine the numerators over the common denominator.

$\frac{2 g \cdot 3 - 2 g}{3} + 2 = \frac{5}{3} g$

Simplify the numerator.

Factor $2 g$ out of $2 g \cdot 3 - 2 g$ .

Factor $2 g$ out of $2 g \cdot 3$ .

$\frac{2 g (3) - 2 g}{3} + 2 = \frac{5}{3} g$

Factor $2 g$ out of $- 2 g$ .

$\frac{2 g (3) + 2 g (- 1)}{3} + 2 = \frac{5}{3} g$

Factor $2 g$ out of $2 g (3) + 2 g (- 1)$ .

$\frac{2 g (3 - 1)}{3} + 2 = \frac{5}{3} g$

Subtract $1$ from $3$ .

$\frac{2 g \cdot 2}{3} + 2 = \frac{5}{3} g$

Multiply $2$ by $2$ .

$\frac{4 g}{3} + 2 = \frac{5}{3} g$

Step 3

Combine $\frac{5}{3}$ and $g$ .

$\frac{4 g}{3} + 2 = \frac{5 g}{3}$

Step 4

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

Subtract $\frac{5 g}{3}$ from both sides of the equation.

$\frac{4 g}{3} + 2 - \frac{5 g}{3} = 0$

Combine the numerators over the common denominator.

$2 + \frac{4 g - 5 g}{3} = 0$

Subtract $5 g$ from $4 g$ .

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

Move the negative in front of the fraction.

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

Step 5

Subtract $2$ from both sides of the equation.

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

Step 6

Multiply both sides of the equation by $- 3$ .

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

Step 7

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{g}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{g}{3}$ into the numerator.

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - g = - 3 \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 g = - 3 \cdot - 2$

Multiply $g$ by $1$ .

$g = - 3 \cdot - 2$

Simplify the right side.

Multiply $- 3$ by $- 2$ .

$g = 6$

Solve for g 5/3g=2g-2/3g+2

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