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Simplifying 3 + -1(8v + -5) + (6 + -7v) + -1 = 7 + -1(v + -1) + (4v + 4) Reorder the terms: 3 + -1(-5 + 8v) + (6 + -7v) + -1 = 7 + -1(v + -1) + (4v + 4) 3 + (-5 * -1 + 8v * -1) + (6 + -7v) + -1 = 7 + -1(v + -1) + (4v + 4) 3 + (5 + -8v) + (6 + -7v) + -1 = 7 + -1(v + -1) + (4v + 4) Remove parenthesis around (6 + -7v) 3 + 5 + -8v + 6 + -7v + -1 = 7 + -1(v + -1) + (4v + 4) Reorder the terms: 3 + 5 + 6 + -1 + -8v + -7v = 7 + -1(v + -1) + (4v + 4) Combine like terms: 3 + 5 = 8 8 + 6 + -1 + -8v + -7v = 7 + -1(v + -1) + (4v + 4) Combine like terms: 8 + 6 = 14 14 + -1 + -8v + -7v = 7 + -1(v + -1) + (4v + 4) Combine like terms: 14 + -1 = 13 13 + -8v + -7v = 7 + -1(v + -1) + (4v + 4) Combine like terms: -8v + -7v = -15v 13 + -15v = 7 + -1(v + -1) + (4v + 4) Reorder the terms: 13 + -15v = 7 + -1(-1 + v) + (4v + 4) 13 + -15v = 7 + (-1 * -1 + v * -1) + (4v + 4) 13 + -15v = 7 + (1 + -1v) + (4v + 4) Reorder the terms: 13 + -15v = 7 + 1 + -1v + (4 + 4v) Remove parenthesis around (4 + 4v) 13 + -15v = 7 + 1 + -1v + 4 + 4v Reorder the terms: 13 + -15v = 7 + 1 + 4 + -1v + 4v Combine like terms: 7 + 1 = 8 13 + -15v = 8 + 4 + -1v + 4v Combine like terms: 8 + 4 = 12 13 + -15v = 12 + -1v + 4v Combine like terms: -1v + 4v = 3v 13 + -15v = 12 + 3v Solving 13 + -15v = 12 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. 13 + -15v + -3v = 12 + 3v + -3v Combine like terms: -15v + -3v = -18v 13 + -18v = 12 + 3v + -3v Combine like terms: 3v + -3v = 0 13 + -18v = 12 + 0 13 + -18v = 12 Add '-13' to each side of the equation. 13 + -13 + -18v = 12 + -13 Combine like terms: 13 + -13 = 0 0 + -18v = 12 + -13 -18v = 12 + -13 Combine like terms: 12 + -13 = -1 -18v = -1 Divide each side by '-18'. v = 0.05555555556 Simplifying v = 0.05555555556
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