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Simplifying 6(3v + -1) + 3v = 4(v + 6) + 2v Reorder the terms: 6(-1 + 3v) + 3v = 4(v + 6) + 2v (-1 * 6 + 3v * 6) + 3v = 4(v + 6) + 2v (-6 + 18v) + 3v = 4(v + 6) + 2v Combine like terms: 18v + 3v = 21v -6 + 21v = 4(v + 6) + 2v Reorder the terms: -6 + 21v = 4(6 + v) + 2v -6 + 21v = (6 * 4 + v * 4) + 2v -6 + 21v = (24 + 4v) + 2v Combine like terms: 4v + 2v = 6v -6 + 21v = 24 + 6v Solving -6 + 21v = 24 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. -6 + 21v + -6v = 24 + 6v + -6v Combine like terms: 21v + -6v = 15v -6 + 15v = 24 + 6v + -6v Combine like terms: 6v + -6v = 0 -6 + 15v = 24 + 0 -6 + 15v = 24 Add '6' to each side of the equation. -6 + 6 + 15v = 24 + 6 Combine like terms: -6 + 6 = 0 0 + 15v = 24 + 6 15v = 24 + 6 Combine like terms: 24 + 6 = 30 15v = 30 Divide each side by '15'. v = 2 Simplifying v = 2
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