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Simplifying 4(6 + -4v) + 8(v + 6) = -6v + 4v (6 * 4 + -4v * 4) + 8(v + 6) = -6v + 4v (24 + -16v) + 8(v + 6) = -6v + 4v Reorder the terms: 24 + -16v + 8(6 + v) = -6v + 4v 24 + -16v + (6 * 8 + v * 8) = -6v + 4v 24 + -16v + (48 + 8v) = -6v + 4v Reorder the terms: 24 + 48 + -16v + 8v = -6v + 4v Combine like terms: 24 + 48 = 72 72 + -16v + 8v = -6v + 4v Combine like terms: -16v + 8v = -8v 72 + -8v = -6v + 4v Combine like terms: -6v + 4v = -2v 72 + -8v = -2v Solving 72 + -8v = -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. 72 + -8v + 2v = -2v + 2v Combine like terms: -8v + 2v = -6v 72 + -6v = -2v + 2v Combine like terms: -2v + 2v = 0 72 + -6v = 0 Add '-72' to each side of the equation. 72 + -72 + -6v = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -6v = 0 + -72 -6v = 0 + -72 Combine like terms: 0 + -72 = -72 -6v = -72 Divide each side by '-6'. v = 12 Simplifying v = 12
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