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Simplifying 3(7v + 8) + -9 = 14 + -2v + 6(3v + -4) Reorder the terms: 3(8 + 7v) + -9 = 14 + -2v + 6(3v + -4) (8 * 3 + 7v * 3) + -9 = 14 + -2v + 6(3v + -4) (24 + 21v) + -9 = 14 + -2v + 6(3v + -4) Reorder the terms: 24 + -9 + 21v = 14 + -2v + 6(3v + -4) Combine like terms: 24 + -9 = 15 15 + 21v = 14 + -2v + 6(3v + -4) Reorder the terms: 15 + 21v = 14 + -2v + 6(-4 + 3v) 15 + 21v = 14 + -2v + (-4 * 6 + 3v * 6) 15 + 21v = 14 + -2v + (-24 + 18v) Reorder the terms: 15 + 21v = 14 + -24 + -2v + 18v Combine like terms: 14 + -24 = -10 15 + 21v = -10 + -2v + 18v Combine like terms: -2v + 18v = 16v 15 + 21v = -10 + 16v Solving 15 + 21v = -10 + 16v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-16v' to each side of the equation. 15 + 21v + -16v = -10 + 16v + -16v Combine like terms: 21v + -16v = 5v 15 + 5v = -10 + 16v + -16v Combine like terms: 16v + -16v = 0 15 + 5v = -10 + 0 15 + 5v = -10 Add '-15' to each side of the equation. 15 + -15 + 5v = -10 + -15 Combine like terms: 15 + -15 = 0 0 + 5v = -10 + -15 5v = -10 + -15 Combine like terms: -10 + -15 = -25 5v = -25 Divide each side by '5'. v = -5 Simplifying v = -5
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