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Simplifying 8(v + 1) = 2(1 + -4v) + -9 Reorder the terms: 8(1 + v) = 2(1 + -4v) + -9 (1 * 8 + v * 8) = 2(1 + -4v) + -9 (8 + 8v) = 2(1 + -4v) + -9 8 + 8v = (1 * 2 + -4v * 2) + -9 8 + 8v = (2 + -8v) + -9 Reorder the terms: 8 + 8v = 2 + -9 + -8v Combine like terms: 2 + -9 = -7 8 + 8v = -7 + -8v Solving 8 + 8v = -7 + -8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '8v' to each side of the equation. 8 + 8v + 8v = -7 + -8v + 8v Combine like terms: 8v + 8v = 16v 8 + 16v = -7 + -8v + 8v Combine like terms: -8v + 8v = 0 8 + 16v = -7 + 0 8 + 16v = -7 Add '-8' to each side of the equation. 8 + -8 + 16v = -7 + -8 Combine like terms: 8 + -8 = 0 0 + 16v = -7 + -8 16v = -7 + -8 Combine like terms: -7 + -8 = -15 16v = -15 Divide each side by '16'. v = -0.9375 Simplifying v = -0.9375
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