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Simplifying -3v + 8(v + 9) = -12(5 + -2v) + 3v Reorder the terms: -3v + 8(9 + v) = -12(5 + -2v) + 3v -3v + (9 * 8 + v * 8) = -12(5 + -2v) + 3v -3v + (72 + 8v) = -12(5 + -2v) + 3v Reorder the terms: 72 + -3v + 8v = -12(5 + -2v) + 3v Combine like terms: -3v + 8v = 5v 72 + 5v = -12(5 + -2v) + 3v 72 + 5v = (5 * -12 + -2v * -12) + 3v 72 + 5v = (-60 + 24v) + 3v Combine like terms: 24v + 3v = 27v 72 + 5v = -60 + 27v Solving 72 + 5v = -60 + 27v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-27v' to each side of the equation. 72 + 5v + -27v = -60 + 27v + -27v Combine like terms: 5v + -27v = -22v 72 + -22v = -60 + 27v + -27v Combine like terms: 27v + -27v = 0 72 + -22v = -60 + 0 72 + -22v = -60 Add '-72' to each side of the equation. 72 + -72 + -22v = -60 + -72 Combine like terms: 72 + -72 = 0 0 + -22v = -60 + -72 -22v = -60 + -72 Combine like terms: -60 + -72 = -132 -22v = -132 Divide each side by '-22'. v = 6 Simplifying v = 6
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