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Simplifying -6(v + 3) + 4v + 6 = 6v + 7 Reorder the terms: -6(3 + v) + 4v + 6 = 6v + 7 (3 * -6 + v * -6) + 4v + 6 = 6v + 7 (-18 + -6v) + 4v + 6 = 6v + 7 Reorder the terms: -18 + 6 + -6v + 4v = 6v + 7 Combine like terms: -18 + 6 = -12 -12 + -6v + 4v = 6v + 7 Combine like terms: -6v + 4v = -2v -12 + -2v = 6v + 7 Reorder the terms: -12 + -2v = 7 + 6v Solving -12 + -2v = 7 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. -12 + -2v + -6v = 7 + 6v + -6v Combine like terms: -2v + -6v = -8v -12 + -8v = 7 + 6v + -6v Combine like terms: 6v + -6v = 0 -12 + -8v = 7 + 0 -12 + -8v = 7 Add '12' to each side of the equation. -12 + 12 + -8v = 7 + 12 Combine like terms: -12 + 12 = 0 0 + -8v = 7 + 12 -8v = 7 + 12 Combine like terms: 7 + 12 = 19 -8v = 19 Divide each side by '-8'. v = -2.375 Simplifying v = -2.375
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