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