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Simplifying 14(v + 3) + -2v = 3(v + 4) + -15 Reorder the terms: 14(3 + v) + -2v = 3(v + 4) + -15 (3 * 14 + v * 14) + -2v = 3(v + 4) + -15 (42 + 14v) + -2v = 3(v + 4) + -15 Combine like terms: 14v + -2v = 12v 42 + 12v = 3(v + 4) + -15 Reorder the terms: 42 + 12v = 3(4 + v) + -15 42 + 12v = (4 * 3 + v * 3) + -15 42 + 12v = (12 + 3v) + -15 Reorder the terms: 42 + 12v = 12 + -15 + 3v Combine like terms: 12 + -15 = -3 42 + 12v = -3 + 3v Solving 42 + 12v = -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. 42 + 12v + -3v = -3 + 3v + -3v Combine like terms: 12v + -3v = 9v 42 + 9v = -3 + 3v + -3v Combine like terms: 3v + -3v = 0 42 + 9v = -3 + 0 42 + 9v = -3 Add '-42' to each side of the equation. 42 + -42 + 9v = -3 + -42 Combine like terms: 42 + -42 = 0 0 + 9v = -3 + -42 9v = -3 + -42 Combine like terms: -3 + -42 = -45 9v = -45 Divide each side by '9'. v = -5 Simplifying v = -5
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