Solve for v. 5v – 1/2 = 4 + 3/2 v v =

To solve for ( v ) in the equation ( 5v – frac{1}{2} = 4 + frac{3}{2} v ), follow these steps:

1. Isolate terms involving ( v ): Start by moving all the ( v ) terms to one side of the equation. Subtract (frac{3}{2} v) from both sides:

[

5v – frac{3}{2} v – frac{1}{2} = 4

]

2. Combine like terms: Convert ( 5v ) to a fraction for easier calculation. Since ( 5 = frac{10}{2} ):

[

left(frac{10}{2} v – frac{3}{2} vright) – frac{1}{2} = 4

]

This simplifies to:

[

frac{7}{2} v – frac{1}{2} = 4

]

3. Add (frac{1}{2}) to both sides:

[

frac{7}{2} v = 4 + frac{1}{2}

]

Convert 4 to halves: ( 4 = frac{8}{2} ):

[

frac{7}{2