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Simplifying 2(3v + 1) + 7v + 7 = 6(v + -4) + -4v Reorder the terms: 2(1 + 3v) + 7v + 7 = 6(v + -4) + -4v (1 * 2 + 3v * 2) + 7v + 7 = 6(v + -4) + -4v (2 + 6v) + 7v + 7 = 6(v + -4) + -4v Reorder the terms: 2 + 7 + 6v + 7v = 6(v + -4) + -4v Combine like terms: 2 + 7 = 9 9 + 6v + 7v = 6(v + -4) + -4v Combine like terms: 6v + 7v = 13v 9 + 13v = 6(v + -4) + -4v Reorder the terms: 9 + 13v = 6(-4 + v) + -4v 9 + 13v = (-4 * 6 + v * 6) + -4v 9 + 13v = (-24 + 6v) + -4v Combine like terms: 6v + -4v = 2v 9 + 13v = -24 + 2v Solving 9 + 13v = -24 + 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. 9 + 13v + -2v = -24 + 2v + -2v Combine like terms: 13v + -2v = 11v 9 + 11v = -24 + 2v + -2v Combine like terms: 2v + -2v = 0 9 + 11v = -24 + 0 9 + 11v = -24 Add '-9' to each side of the equation. 9 + -9 + 11v = -24 + -9 Combine like terms: 9 + -9 = 0 0 + 11v = -24 + -9 11v = -24 + -9 Combine like terms: -24 + -9 = -33 11v = -33 Divide each side by '11'. v = -3 Simplifying v = -3
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