Question

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

Explanation:

Step1: Distribute the 2 on the right side

We use the distributive property \(a(b + c)=ab+ac\). Here, \(a = 2\), \(b=\frac{1}{3}y\) and \(c=- 3\). So we get:
\(-2 + y=2\times\frac{1}{3}y-2\times3\)
\(-2 + y=\frac{2}{3}y-6\)

Step2: Subtract \(\frac{2}{3}y\) from both sides

To get all the \(y\) terms on one side, we subtract \(\frac{2}{3}y\) from both sides of the equation:
\(-2 + y-\frac{2}{3}y=\frac{2}{3}y-6-\frac{2}{3}y\)
Simplifying the left side: \(y-\frac{2}{3}y=\frac{3y - 2y}{3}=\frac{1}{3}y\), and the right side \(\frac{2}{3}y-\frac{2}{3}y = 0\), so we have:
\(-2+\frac{1}{3}y=-6\)

Step3: Add 2 to both sides

To isolate the term with \(y\), we add 2 to both sides of the equation:
\(-2+\frac{1}{3}y + 2=-6 + 2\)
Simplifying, we get:
\(\frac{1}{3}y=-4\)

Step4: Multiply both sides by 3

To solve for \(y\), we multiply both sides of the equation by 3:
\(3\times\frac{1}{3}y=3\times(-4)\)
Since \(3\times\frac{1}{3}y = y\) and \(3\times(-4)=- 12\), we have:
\(y=-12\)

Answer:

\(-12\)