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Simplifying 12(v + 1) + -3v = (3v + 4) + -19 Reorder the terms: 12(1 + v) + -3v = (3v + 4) + -19 (1 * 12 + v * 12) + -3v = (3v + 4) + -19 (12 + 12v) + -3v = (3v + 4) + -19 Combine like terms: 12v + -3v = 9v 12 + 9v = (3v + 4) + -19 Reorder the terms: 12 + 9v = (4 + 3v) + -19 Remove parenthesis around (4 + 3v) 12 + 9v = 4 + 3v + -19 Reorder the terms: 12 + 9v = 4 + -19 + 3v Combine like terms: 4 + -19 = -15 12 + 9v = -15 + 3v Solving 12 + 9v = -15 + 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 = -15 + 3v + -3v Combine like terms: 9v + -3v = 6v 12 + 6v = -15 + 3v + -3v Combine like terms: 3v + -3v = 0 12 + 6v = -15 + 0 12 + 6v = -15 Add '-12' to each side of the equation. 12 + -12 + 6v = -15 + -12 Combine like terms: 12 + -12 = 0 0 + 6v = -15 + -12 6v = -15 + -12 Combine like terms: -15 + -12 = -27 6v = -27 Divide each side by '6'. v = -4.5 Simplifying v = -4.5
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