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Simplifying 8(v + 9) + -1(9 + 3v) = -7v + 9 + -6 + 9v Reorder the terms: 8(9 + v) + -1(9 + 3v) = -7v + 9 + -6 + 9v (9 * 8 + v * 8) + -1(9 + 3v) = -7v + 9 + -6 + 9v (72 + 8v) + -1(9 + 3v) = -7v + 9 + -6 + 9v 72 + 8v + (9 * -1 + 3v * -1) = -7v + 9 + -6 + 9v 72 + 8v + (-9 + -3v) = -7v + 9 + -6 + 9v Reorder the terms: 72 + -9 + 8v + -3v = -7v + 9 + -6 + 9v Combine like terms: 72 + -9 = 63 63 + 8v + -3v = -7v + 9 + -6 + 9v Combine like terms: 8v + -3v = 5v 63 + 5v = -7v + 9 + -6 + 9v Reorder the terms: 63 + 5v = 9 + -6 + -7v + 9v Combine like terms: 9 + -6 = 3 63 + 5v = 3 + -7v + 9v Combine like terms: -7v + 9v = 2v 63 + 5v = 3 + 2v Solving 63 + 5v = 3 + 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. 63 + 5v + -2v = 3 + 2v + -2v Combine like terms: 5v + -2v = 3v 63 + 3v = 3 + 2v + -2v Combine like terms: 2v + -2v = 0 63 + 3v = 3 + 0 63 + 3v = 3 Add '-63' to each side of the equation. 63 + -63 + 3v = 3 + -63 Combine like terms: 63 + -63 = 0 0 + 3v = 3 + -63 3v = 3 + -63 Combine like terms: 3 + -63 = -60 3v = -60 Divide each side by '3'. v = -20 Simplifying v = -20
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