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Simplifying 12(v + 1) + -3v = 3(v + 4) + -16 Reorder the terms: 12(1 + v) + -3v = 3(v + 4) + -16 (1 * 12 + v * 12) + -3v = 3(v + 4) + -16 (12 + 12v) + -3v = 3(v + 4) + -16 Combine like terms: 12v + -3v = 9v 12 + 9v = 3(v + 4) + -16 Reorder the terms: 12 + 9v = 3(4 + v) + -16 12 + 9v = (4 * 3 + v * 3) + -16 12 + 9v = (12 + 3v) + -16 Reorder the terms: 12 + 9v = 12 + -16 + 3v Combine like terms: 12 + -16 = -4 12 + 9v = -4 + 3v Solving 12 + 9v = -4 + 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. 12 + 9v + -3v = -4 + 3v + -3v Combine like terms: 9v + -3v = 6v 12 + 6v = -4 + 3v + -3v Combine like terms: 3v + -3v = 0 12 + 6v = -4 + 0 12 + 6v = -4 Add '-12' to each side of the equation. 12 + -12 + 6v = -4 + -12 Combine like terms: 12 + -12 = 0 0 + 6v = -4 + -12 6v = -4 + -12 Combine like terms: -4 + -12 = -16 6v = -16 Divide each side by '6'. v = -2.666666667 Simplifying v = -2.666666667
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