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Simplifying 12(v + 3) + -3v = 3(v + 2) + -9 Reorder the terms: 12(3 + v) + -3v = 3(v + 2) + -9 (3 * 12 + v * 12) + -3v = 3(v + 2) + -9 (36 + 12v) + -3v = 3(v + 2) + -9 Combine like terms: 12v + -3v = 9v 36 + 9v = 3(v + 2) + -9 Reorder the terms: 36 + 9v = 3(2 + v) + -9 36 + 9v = (2 * 3 + v * 3) + -9 36 + 9v = (6 + 3v) + -9 Reorder the terms: 36 + 9v = 6 + -9 + 3v Combine like terms: 6 + -9 = -3 36 + 9v = -3 + 3v Solving 36 + 9v = -3 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. 36 + 9v + -3v = -3 + 3v + -3v Combine like terms: 9v + -3v = 6v 36 + 6v = -3 + 3v + -3v Combine like terms: 3v + -3v = 0 36 + 6v = -3 + 0 36 + 6v = -3 Add '-36' to each side of the equation. 36 + -36 + 6v = -3 + -36 Combine like terms: 36 + -36 = 0 0 + 6v = -3 + -36 6v = -3 + -36 Combine like terms: -3 + -36 = -39 6v = -39 Divide each side by '6'. v = -6.5 Simplifying v = -6.5
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