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Simplifying 8v + 5 + 6v + -5 = 9(1 + 2v) + 3(4 + v) Reorder the terms: 5 + -5 + 8v + 6v = 9(1 + 2v) + 3(4 + v) Combine like terms: 5 + -5 = 0 0 + 8v + 6v = 9(1 + 2v) + 3(4 + v) 8v + 6v = 9(1 + 2v) + 3(4 + v) Combine like terms: 8v + 6v = 14v 14v = 9(1 + 2v) + 3(4 + v) 14v = (1 * 9 + 2v * 9) + 3(4 + v) 14v = (9 + 18v) + 3(4 + v) 14v = 9 + 18v + (4 * 3 + v * 3) 14v = 9 + 18v + (12 + 3v) Reorder the terms: 14v = 9 + 12 + 18v + 3v Combine like terms: 9 + 12 = 21 14v = 21 + 18v + 3v Combine like terms: 18v + 3v = 21v 14v = 21 + 21v Solving 14v = 21 + 21v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-21v' to each side of the equation. 14v + -21v = 21 + 21v + -21v Combine like terms: 14v + -21v = -7v -7v = 21 + 21v + -21v Combine like terms: 21v + -21v = 0 -7v = 21 + 0 -7v = 21 Divide each side by '-7'. v = -3 Simplifying v = -3
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