Solve for v: 1/2 + 8 = 3 – 1/3 v. v = ___. Submit.

To solve the equation ( frac{1}{2} + 8 = 3 – frac{1}{3} v ), follow these steps:

1. Combine like terms on the left side:

[

frac{1}{2} + 8 = frac{1}{2} + frac{16}{2} = frac{17}{2}

]

So, the equation becomes:

[

frac{17}{2} = 3 – frac{1}{3} v

]

2. Isolate the term with ( v ) on one side. First, subtract 3 from both sides:

[

frac{17}{2} – 3 = -frac{1}{3} v

]

Convert 3 to a fraction with a denominator of 2:

[

3 = frac{6}{2} Rightarrow frac{17}{2} – frac{6}{2} = frac{11}{2}

]

So, now we have:

[

frac{11}{2} = -frac{1}{3} v

]

3. Multiply both sides by ( -3 ) to solve for ( v ):

[

v = -3 times frac{11}{2} =