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Simplifying 5(v + 1) + -1 = 3(v + -1) + 7 Reorder the terms: 5(1 + v) + -1 = 3(v + -1) + 7 (1 * 5 + v * 5) + -1 = 3(v + -1) + 7 (5 + 5v) + -1 = 3(v + -1) + 7 Reorder the terms: 5 + -1 + 5v = 3(v + -1) + 7 Combine like terms: 5 + -1 = 4 4 + 5v = 3(v + -1) + 7 Reorder the terms: 4 + 5v = 3(-1 + v) + 7 4 + 5v = (-1 * 3 + v * 3) + 7 4 + 5v = (-3 + 3v) + 7 Reorder the terms: 4 + 5v = -3 + 7 + 3v Combine like terms: -3 + 7 = 4 4 + 5v = 4 + 3v Add '-4' to each side of the equation. 4 + -4 + 5v = 4 + -4 + 3v Combine like terms: 4 + -4 = 0 0 + 5v = 4 + -4 + 3v 5v = 4 + -4 + 3v Combine like terms: 4 + -4 = 0 5v = 0 + 3v 5v = 3v Solving 5v = 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. 5v + -3v = 3v + -3v Combine like terms: 5v + -3v = 2v 2v = 3v + -3v Combine like terms: 3v + -3v = 0 2v = 0 Divide each side by '2'. v = 0 Simplifying v = 0
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