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Simplifying 14(v + 1) = 4(3v + 2) + -12 Reorder the terms: 14(1 + v) = 4(3v + 2) + -12 (1 * 14 + v * 14) = 4(3v + 2) + -12 (14 + 14v) = 4(3v + 2) + -12 Reorder the terms: 14 + 14v = 4(2 + 3v) + -12 14 + 14v = (2 * 4 + 3v * 4) + -12 14 + 14v = (8 + 12v) + -12 Reorder the terms: 14 + 14v = 8 + -12 + 12v Combine like terms: 8 + -12 = -4 14 + 14v = -4 + 12v Solving 14 + 14v = -4 + 12v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12v' to each side of the equation. 14 + 14v + -12v = -4 + 12v + -12v Combine like terms: 14v + -12v = 2v 14 + 2v = -4 + 12v + -12v Combine like terms: 12v + -12v = 0 14 + 2v = -4 + 0 14 + 2v = -4 Add '-14' to each side of the equation. 14 + -14 + 2v = -4 + -14 Combine like terms: 14 + -14 = 0 0 + 2v = -4 + -14 2v = -4 + -14 Combine like terms: -4 + -14 = -18 2v = -18 Divide each side by '2'. v = -9 Simplifying v = -9
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