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Simplifying -46 = 7(6 + 7v) + 2(1 + -2v) -46 = (6 * 7 + 7v * 7) + 2(1 + -2v) -46 = (42 + 49v) + 2(1 + -2v) -46 = 42 + 49v + (1 * 2 + -2v * 2) -46 = 42 + 49v + (2 + -4v) Reorder the terms: -46 = 42 + 2 + 49v + -4v Combine like terms: 42 + 2 = 44 -46 = 44 + 49v + -4v Combine like terms: 49v + -4v = 45v -46 = 44 + 45v Solving -46 = 44 + 45v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-45v' to each side of the equation. -46 + -45v = 44 + 45v + -45v Combine like terms: 45v + -45v = 0 -46 + -45v = 44 + 0 -46 + -45v = 44 Add '46' to each side of the equation. -46 + 46 + -45v = 44 + 46 Combine like terms: -46 + 46 = 0 0 + -45v = 44 + 46 -45v = 44 + 46 Combine like terms: 44 + 46 = 90 -45v = 90 Divide each side by '-45'. v = -2 Simplifying v = -2
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