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Simplifying 2(v + 3) + 4(-4v + -6) = -1 + -4v + 7v Reorder the terms: 2(3 + v) + 4(-4v + -6) = -1 + -4v + 7v (3 * 2 + v * 2) + 4(-4v + -6) = -1 + -4v + 7v (6 + 2v) + 4(-4v + -6) = -1 + -4v + 7v Reorder the terms: 6 + 2v + 4(-6 + -4v) = -1 + -4v + 7v 6 + 2v + (-6 * 4 + -4v * 4) = -1 + -4v + 7v 6 + 2v + (-24 + -16v) = -1 + -4v + 7v Reorder the terms: 6 + -24 + 2v + -16v = -1 + -4v + 7v Combine like terms: 6 + -24 = -18 -18 + 2v + -16v = -1 + -4v + 7v Combine like terms: 2v + -16v = -14v -18 + -14v = -1 + -4v + 7v Combine like terms: -4v + 7v = 3v -18 + -14v = -1 + 3v Solving -18 + -14v = -1 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. -18 + -14v + -3v = -1 + 3v + -3v Combine like terms: -14v + -3v = -17v -18 + -17v = -1 + 3v + -3v Combine like terms: 3v + -3v = 0 -18 + -17v = -1 + 0 -18 + -17v = -1 Add '18' to each side of the equation. -18 + 18 + -17v = -1 + 18 Combine like terms: -18 + 18 = 0 0 + -17v = -1 + 18 -17v = -1 + 18 Combine like terms: -1 + 18 = 17 -17v = 17 Divide each side by '-17'. v = -1 Simplifying v = -1
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