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Simplifying 14(v + 1) + -2 = 4(3v + 1) + -7 Reorder the terms: 14(1 + v) + -2 = 4(3v + 1) + -7 (1 * 14 + v * 14) + -2 = 4(3v + 1) + -7 (14 + 14v) + -2 = 4(3v + 1) + -7 Reorder the terms: 14 + -2 + 14v = 4(3v + 1) + -7 Combine like terms: 14 + -2 = 12 12 + 14v = 4(3v + 1) + -7 Reorder the terms: 12 + 14v = 4(1 + 3v) + -7 12 + 14v = (1 * 4 + 3v * 4) + -7 12 + 14v = (4 + 12v) + -7 Reorder the terms: 12 + 14v = 4 + -7 + 12v Combine like terms: 4 + -7 = -3 12 + 14v = -3 + 12v Solving 12 + 14v = -3 + 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. 12 + 14v + -12v = -3 + 12v + -12v Combine like terms: 14v + -12v = 2v 12 + 2v = -3 + 12v + -12v Combine like terms: 12v + -12v = 0 12 + 2v = -3 + 0 12 + 2v = -3 Add '-12' to each side of the equation. 12 + -12 + 2v = -3 + -12 Combine like terms: 12 + -12 = 0 0 + 2v = -3 + -12 2v = -3 + -12 Combine like terms: -3 + -12 = -15 2v = -15 Divide each side by '2'. v = -7.5 Simplifying v = -7.5
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