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Simplifying -1(1 + 2v) = 2v + 31 (1 * -1 + 2v * -1) = 2v + 31 (-1 + -2v) = 2v + 31 Reorder the terms: -1 + -2v = 31 + 2v Solving -1 + -2v = 31 + 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. -1 + -2v + -2v = 31 + 2v + -2v Combine like terms: -2v + -2v = -4v -1 + -4v = 31 + 2v + -2v Combine like terms: 2v + -2v = 0 -1 + -4v = 31 + 0 -1 + -4v = 31 Add '1' to each side of the equation. -1 + 1 + -4v = 31 + 1 Combine like terms: -1 + 1 = 0 0 + -4v = 31 + 1 -4v = 31 + 1 Combine like terms: 31 + 1 = 32 -4v = 32 Divide each side by '-4'. v = -8 Simplifying v = -8
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