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Simplifying 9 + -1(v + -3) + 4v = 4v + -5(v + 2) + -6 Reorder the terms: 9 + -1(-3 + v) + 4v = 4v + -5(v + 2) + -6 9 + (-3 * -1 + v * -1) + 4v = 4v + -5(v + 2) + -6 9 + (3 + -1v) + 4v = 4v + -5(v + 2) + -6 Combine like terms: 9 + 3 = 12 12 + -1v + 4v = 4v + -5(v + 2) + -6 Combine like terms: -1v + 4v = 3v 12 + 3v = 4v + -5(v + 2) + -6 Reorder the terms: 12 + 3v = 4v + -5(2 + v) + -6 12 + 3v = 4v + (2 * -5 + v * -5) + -6 12 + 3v = 4v + (-10 + -5v) + -6 Reorder the terms: 12 + 3v = -10 + -6 + 4v + -5v Combine like terms: -10 + -6 = -16 12 + 3v = -16 + 4v + -5v Combine like terms: 4v + -5v = -1v 12 + 3v = -16 + -1v Solving 12 + 3v = -16 + -1v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add 'v' to each side of the equation. 12 + 3v + v = -16 + -1v + v Combine like terms: 3v + v = 4v 12 + 4v = -16 + -1v + v Combine like terms: -1v + v = 0 12 + 4v = -16 + 0 12 + 4v = -16 Add '-12' to each side of the equation. 12 + -12 + 4v = -16 + -12 Combine like terms: 12 + -12 = 0 0 + 4v = -16 + -12 4v = -16 + -12 Combine like terms: -16 + -12 = -28 4v = -28 Divide each side by '4'. v = -7 Simplifying v = -7
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