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Simplifying 12 + -4v + 5v = 10 + v + -6 + -3v Combine like terms: -4v + 5v = 1v 12 + 1v = 10 + v + -6 + -3v Reorder the terms: 12 + 1v = 10 + -6 + v + -3v Combine like terms: 10 + -6 = 4 12 + 1v = 4 + v + -3v Combine like terms: v + -3v = -2v 12 + 1v = 4 + -2v Solving 12 + 1v = 4 + -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. 12 + 1v + 2v = 4 + -2v + 2v Combine like terms: 1v + 2v = 3v 12 + 3v = 4 + -2v + 2v Combine like terms: -2v + 2v = 0 12 + 3v = 4 + 0 12 + 3v = 4 Add '-12' to each side of the equation. 12 + -12 + 3v = 4 + -12 Combine like terms: 12 + -12 = 0 0 + 3v = 4 + -12 3v = 4 + -12 Combine like terms: 4 + -12 = -8 3v = -8 Divide each side by '3'. v = -2.666666667 Simplifying v = -2.666666667
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