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Simplifying 3(3v + 3) + 3v + 7 = 6(v + 1) + -4v Reorder the terms: 3(3 + 3v) + 3v + 7 = 6(v + 1) + -4v (3 * 3 + 3v * 3) + 3v + 7 = 6(v + 1) + -4v (9 + 9v) + 3v + 7 = 6(v + 1) + -4v Reorder the terms: 9 + 7 + 9v + 3v = 6(v + 1) + -4v Combine like terms: 9 + 7 = 16 16 + 9v + 3v = 6(v + 1) + -4v Combine like terms: 9v + 3v = 12v 16 + 12v = 6(v + 1) + -4v Reorder the terms: 16 + 12v = 6(1 + v) + -4v 16 + 12v = (1 * 6 + v * 6) + -4v 16 + 12v = (6 + 6v) + -4v Combine like terms: 6v + -4v = 2v 16 + 12v = 6 + 2v Solving 16 + 12v = 6 + 2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2v' to each side of the equation. 16 + 12v + -2v = 6 + 2v + -2v Combine like terms: 12v + -2v = 10v 16 + 10v = 6 + 2v + -2v Combine like terms: 2v + -2v = 0 16 + 10v = 6 + 0 16 + 10v = 6 Add '-16' to each side of the equation. 16 + -16 + 10v = 6 + -16 Combine like terms: 16 + -16 = 0 0 + 10v = 6 + -16 10v = 6 + -16 Combine like terms: 6 + -16 = -10 10v = -10 Divide each side by '10'. v = -1 Simplifying v = -1
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