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Simplifying 2(3v + -2) + 6v = 6(v + 2) + 4v Reorder the terms: 2(-2 + 3v) + 6v = 6(v + 2) + 4v (-2 * 2 + 3v * 2) + 6v = 6(v + 2) + 4v (-4 + 6v) + 6v = 6(v + 2) + 4v Combine like terms: 6v + 6v = 12v -4 + 12v = 6(v + 2) + 4v Reorder the terms: -4 + 12v = 6(2 + v) + 4v -4 + 12v = (2 * 6 + v * 6) + 4v -4 + 12v = (12 + 6v) + 4v Combine like terms: 6v + 4v = 10v -4 + 12v = 12 + 10v Solving -4 + 12v = 12 + 10v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10v' to each side of the equation. -4 + 12v + -10v = 12 + 10v + -10v Combine like terms: 12v + -10v = 2v -4 + 2v = 12 + 10v + -10v Combine like terms: 10v + -10v = 0 -4 + 2v = 12 + 0 -4 + 2v = 12 Add '4' to each side of the equation. -4 + 4 + 2v = 12 + 4 Combine like terms: -4 + 4 = 0 0 + 2v = 12 + 4 2v = 12 + 4 Combine like terms: 12 + 4 = 16 2v = 16 Divide each side by '2'. v = 8 Simplifying v = 8
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