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Simplifying 6v + 3v = 3(v + 1) + 5(v + -1) Combine like terms: 6v + 3v = 9v 9v = 3(v + 1) + 5(v + -1) Reorder the terms: 9v = 3(1 + v) + 5(v + -1) 9v = (1 * 3 + v * 3) + 5(v + -1) 9v = (3 + 3v) + 5(v + -1) Reorder the terms: 9v = 3 + 3v + 5(-1 + v) 9v = 3 + 3v + (-1 * 5 + v * 5) 9v = 3 + 3v + (-5 + 5v) Reorder the terms: 9v = 3 + -5 + 3v + 5v Combine like terms: 3 + -5 = -2 9v = -2 + 3v + 5v Combine like terms: 3v + 5v = 8v 9v = -2 + 8v Solving 9v = -2 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. 9v + -8v = -2 + 8v + -8v Combine like terms: 9v + -8v = 1v 1v = -2 + 8v + -8v Combine like terms: 8v + -8v = 0 1v = -2 + 0 1v = -2 Divide each side by '1'. v = -2 Simplifying v = -2
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