Solve for v.
5v – 1/2 = 4 + 3/2 v
v =
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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