solve for g. \n\\( \\frac { 5 } { 3 } g = 2 g - \\frac { 2 } { 3 } g + 2 \\)

Explanation:

Step1: Simplify the right - hand side of the equation

Combine like terms: $$2g-\frac{2}{3}g=\frac{6g - 2g}{3}=\frac{4g}{3}$$ The equation becomes $\frac{5}{3}g=\frac{4}{3}g + 2$.

Step2: Subtract $\frac{4}{3}g$ from both sides

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

Step3: Solve for $g$

Multiply both sides by 3: $$g = 2\times3$$

Answer:

$6$