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Simplifying 5(v + 1) + -1v = 3(v + -1) + 7 Reorder the terms: 5(1 + v) + -1v = 3(v + -1) + 7 (1 * 5 + v * 5) + -1v = 3(v + -1) + 7 (5 + 5v) + -1v = 3(v + -1) + 7 Combine like terms: 5v + -1v = 4v 5 + 4v = 3(v + -1) + 7 Reorder the terms: 5 + 4v = 3(-1 + v) + 7 5 + 4v = (-1 * 3 + v * 3) + 7 5 + 4v = (-3 + 3v) + 7 Reorder the terms: 5 + 4v = -3 + 7 + 3v Combine like terms: -3 + 7 = 4 5 + 4v = 4 + 3v Solving 5 + 4v = 4 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. 5 + 4v + -3v = 4 + 3v + -3v Combine like terms: 4v + -3v = 1v 5 + 1v = 4 + 3v + -3v Combine like terms: 3v + -3v = 0 5 + 1v = 4 + 0 5 + 1v = 4 Add '-5' to each side of the equation. 5 + -5 + 1v = 4 + -5 Combine like terms: 5 + -5 = 0 0 + 1v = 4 + -5 1v = 4 + -5 Combine like terms: 4 + -5 = -1 1v = -1 Divide each side by '1'. v = -1 Simplifying v = -1
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