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Simplifying -6(v + 4) + 3v + 6 = 8v + 12 Reorder the terms: -6(4 + v) + 3v + 6 = 8v + 12 (4 * -6 + v * -6) + 3v + 6 = 8v + 12 (-24 + -6v) + 3v + 6 = 8v + 12 Reorder the terms: -24 + 6 + -6v + 3v = 8v + 12 Combine like terms: -24 + 6 = -18 -18 + -6v + 3v = 8v + 12 Combine like terms: -6v + 3v = -3v -18 + -3v = 8v + 12 Reorder the terms: -18 + -3v = 12 + 8v Solving -18 + -3v = 12 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. -18 + -3v + -8v = 12 + 8v + -8v Combine like terms: -3v + -8v = -11v -18 + -11v = 12 + 8v + -8v Combine like terms: 8v + -8v = 0 -18 + -11v = 12 + 0 -18 + -11v = 12 Add '18' to each side of the equation. -18 + 18 + -11v = 12 + 18 Combine like terms: -18 + 18 = 0 0 + -11v = 12 + 18 -11v = 12 + 18 Combine like terms: 12 + 18 = 30 -11v = 30 Divide each side by '-11'. v = -2.727272727 Simplifying v = -2.727272727
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