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Simplifying -6(v + 3) + 2v + 7 = 5v + 12 Reorder the terms: -6(3 + v) + 2v + 7 = 5v + 12 (3 * -6 + v * -6) + 2v + 7 = 5v + 12 (-18 + -6v) + 2v + 7 = 5v + 12 Reorder the terms: -18 + 7 + -6v + 2v = 5v + 12 Combine like terms: -18 + 7 = -11 -11 + -6v + 2v = 5v + 12 Combine like terms: -6v + 2v = -4v -11 + -4v = 5v + 12 Reorder the terms: -11 + -4v = 12 + 5v Solving -11 + -4v = 12 + 5v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5v' to each side of the equation. -11 + -4v + -5v = 12 + 5v + -5v Combine like terms: -4v + -5v = -9v -11 + -9v = 12 + 5v + -5v Combine like terms: 5v + -5v = 0 -11 + -9v = 12 + 0 -11 + -9v = 12 Add '11' to each side of the equation. -11 + 11 + -9v = 12 + 11 Combine like terms: -11 + 11 = 0 0 + -9v = 12 + 11 -9v = 12 + 11 Combine like terms: 12 + 11 = 23 -9v = 23 Divide each side by '-9'. v = -2.555555556 Simplifying v = -2.555555556
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