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Simplifying 2(2v + 1) + 7v = 6(v + 4) + 3v Reorder the terms: 2(1 + 2v) + 7v = 6(v + 4) + 3v (1 * 2 + 2v * 2) + 7v = 6(v + 4) + 3v (2 + 4v) + 7v = 6(v + 4) + 3v Combine like terms: 4v + 7v = 11v 2 + 11v = 6(v + 4) + 3v Reorder the terms: 2 + 11v = 6(4 + v) + 3v 2 + 11v = (4 * 6 + v * 6) + 3v 2 + 11v = (24 + 6v) + 3v Combine like terms: 6v + 3v = 9v 2 + 11v = 24 + 9v Solving 2 + 11v = 24 + 9v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9v' to each side of the equation. 2 + 11v + -9v = 24 + 9v + -9v Combine like terms: 11v + -9v = 2v 2 + 2v = 24 + 9v + -9v Combine like terms: 9v + -9v = 0 2 + 2v = 24 + 0 2 + 2v = 24 Add '-2' to each side of the equation. 2 + -2 + 2v = 24 + -2 Combine like terms: 2 + -2 = 0 0 + 2v = 24 + -2 2v = 24 + -2 Combine like terms: 24 + -2 = 22 2v = 22 Divide each side by '2'. v = 11 Simplifying v = 11
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