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Simplifying -6(v + 4) + 2v + 7 = 8v + 12 Reorder the terms: -6(4 + v) + 2v + 7 = 8v + 12 (4 * -6 + v * -6) + 2v + 7 = 8v + 12 (-24 + -6v) + 2v + 7 = 8v + 12 Reorder the terms: -24 + 7 + -6v + 2v = 8v + 12 Combine like terms: -24 + 7 = -17 -17 + -6v + 2v = 8v + 12 Combine like terms: -6v + 2v = -4v -17 + -4v = 8v + 12 Reorder the terms: -17 + -4v = 12 + 8v Solving -17 + -4v = 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. -17 + -4v + -8v = 12 + 8v + -8v Combine like terms: -4v + -8v = -12v -17 + -12v = 12 + 8v + -8v Combine like terms: 8v + -8v = 0 -17 + -12v = 12 + 0 -17 + -12v = 12 Add '17' to each side of the equation. -17 + 17 + -12v = 12 + 17 Combine like terms: -17 + 17 = 0 0 + -12v = 12 + 17 -12v = 12 + 17 Combine like terms: 12 + 17 = 29 -12v = 29 Divide each side by '-12'. v = -2.416666667 Simplifying v = -2.416666667
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