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Simplifying (45 + v) * 0.68 = (45 + -1v) * 0.82 Reorder the terms for easier multiplication: 0.68(45 + v) = (45 + -1v) * 0.82 (45 * 0.68 + v * 0.68) = (45 + -1v) * 0.82 (30.6 + 0.68v) = (45 + -1v) * 0.82 Reorder the terms for easier multiplication: 30.6 + 0.68v = 0.82(45 + -1v) 30.6 + 0.68v = (45 * 0.82 + -1v * 0.82) 30.6 + 0.68v = (36.9 + -0.82v) Solving 30.6 + 0.68v = 36.9 + -0.82v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.82v' to each side of the equation. 30.6 + 0.68v + 0.82v = 36.9 + -0.82v + 0.82v Combine like terms: 0.68v + 0.82v = 1.5v 30.6 + 1.5v = 36.9 + -0.82v + 0.82v Combine like terms: -0.82v + 0.82v = 0.00 30.6 + 1.5v = 36.9 + 0.00 30.6 + 1.5v = 36.9 Add '-30.6' to each side of the equation. 30.6 + -30.6 + 1.5v = 36.9 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 0.0 + 1.5v = 36.9 + -30.6 1.5v = 36.9 + -30.6 Combine like terms: 36.9 + -30.6 = 6.3 1.5v = 6.3 Divide each side by '1.5'. v = 4.2 Simplifying v = 4.2
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