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Simplifying -31 = 5(v + -3) + -7v Reorder the terms: -31 = 5(-3 + v) + -7v -31 = (-3 * 5 + v * 5) + -7v -31 = (-15 + 5v) + -7v Combine like terms: 5v + -7v = -2v -31 = -15 + -2v Solving -31 = -15 + -2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2v' to each side of the equation. -31 + 2v = -15 + -2v + 2v Combine like terms: -2v + 2v = 0 -31 + 2v = -15 + 0 -31 + 2v = -15 Add '31' to each side of the equation. -31 + 31 + 2v = -15 + 31 Combine like terms: -31 + 31 = 0 0 + 2v = -15 + 31 2v = -15 + 31 Combine like terms: -15 + 31 = 16 2v = 16 Divide each side by '2'. v = 8 Simplifying v = 8
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