solve for y.\n-2 + y = 2(\\frac{1}{3}y - 3)\n y =

Explanation:

Step1: Expand the right - hand side

Using the distributive property (a(b + c)=ab+ac), we have (2(\frac{1}{3}y-3)=2\times\frac{1}{3}y-2\times3=\frac{2}{3}y - 6). So the equation becomes (-2 + y=\frac{2}{3}y-6).

Step2: Get all (y) terms on one side

Subtract (\frac{2}{3}y) from both sides: (-2 + y-\frac{2}{3}y=\frac{2}{3}y-6-\frac{2}{3}y). Combine like terms: (-2+(1 - \frac{2}{3})y=-6), which simplifies to (-2+\frac{1}{3}y=-6).

Step3: Isolate the (y) term

Add (2) to both sides: (-2+\frac{1}{3}y + 2=-6 + 2). We get (\frac{1}{3}y=-4).

Step4: Solve for (y)

Multiply both sides by (3): (y=-4\times3).

Answer:

(-12)