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Simplifying -7 + -3v + 11 + 12v = 3(4v + 5) + -4(v + 4) Reorder the terms: -7 + 11 + -3v + 12v = 3(4v + 5) + -4(v + 4) Combine like terms: -7 + 11 = 4 4 + -3v + 12v = 3(4v + 5) + -4(v + 4) Combine like terms: -3v + 12v = 9v 4 + 9v = 3(4v + 5) + -4(v + 4) Reorder the terms: 4 + 9v = 3(5 + 4v) + -4(v + 4) 4 + 9v = (5 * 3 + 4v * 3) + -4(v + 4) 4 + 9v = (15 + 12v) + -4(v + 4) Reorder the terms: 4 + 9v = 15 + 12v + -4(4 + v) 4 + 9v = 15 + 12v + (4 * -4 + v * -4) 4 + 9v = 15 + 12v + (-16 + -4v) Reorder the terms: 4 + 9v = 15 + -16 + 12v + -4v Combine like terms: 15 + -16 = -1 4 + 9v = -1 + 12v + -4v Combine like terms: 12v + -4v = 8v 4 + 9v = -1 + 8v Solving 4 + 9v = -1 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. 4 + 9v + -8v = -1 + 8v + -8v Combine like terms: 9v + -8v = 1v 4 + 1v = -1 + 8v + -8v Combine like terms: 8v + -8v = 0 4 + 1v = -1 + 0 4 + 1v = -1 Add '-4' to each side of the equation. 4 + -4 + 1v = -1 + -4 Combine like terms: 4 + -4 = 0 0 + 1v = -1 + -4 1v = -1 + -4 Combine like terms: -1 + -4 = -5 1v = -5 Divide each side by '1'. v = -5 Simplifying v = -5
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