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Simplifying -4(1 + 4v) + 8 = 5(7 + 3v) (1 * -4 + 4v * -4) + 8 = 5(7 + 3v) (-4 + -16v) + 8 = 5(7 + 3v) Reorder the terms: -4 + 8 + -16v = 5(7 + 3v) Combine like terms: -4 + 8 = 4 4 + -16v = 5(7 + 3v) 4 + -16v = (7 * 5 + 3v * 5) 4 + -16v = (35 + 15v) Solving 4 + -16v = 35 + 15v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-15v' to each side of the equation. 4 + -16v + -15v = 35 + 15v + -15v Combine like terms: -16v + -15v = -31v 4 + -31v = 35 + 15v + -15v Combine like terms: 15v + -15v = 0 4 + -31v = 35 + 0 4 + -31v = 35 Add '-4' to each side of the equation. 4 + -4 + -31v = 35 + -4 Combine like terms: 4 + -4 = 0 0 + -31v = 35 + -4 -31v = 35 + -4 Combine like terms: 35 + -4 = 31 -31v = 31 Divide each side by '-31'. v = -1 Simplifying v = -1
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