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Simplifying -2(3v + -6) + 8v = 7 + 3(2v + -3) Reorder the terms: -2(-6 + 3v) + 8v = 7 + 3(2v + -3) (-6 * -2 + 3v * -2) + 8v = 7 + 3(2v + -3) (12 + -6v) + 8v = 7 + 3(2v + -3) Combine like terms: -6v + 8v = 2v 12 + 2v = 7 + 3(2v + -3) Reorder the terms: 12 + 2v = 7 + 3(-3 + 2v) 12 + 2v = 7 + (-3 * 3 + 2v * 3) 12 + 2v = 7 + (-9 + 6v) Combine like terms: 7 + -9 = -2 12 + 2v = -2 + 6v Solving 12 + 2v = -2 + 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 = -2 + 6v + -6v Combine like terms: 2v + -6v = -4v 12 + -4v = -2 + 6v + -6v Combine like terms: 6v + -6v = 0 12 + -4v = -2 + 0 12 + -4v = -2 Add '-12' to each side of the equation. 12 + -12 + -4v = -2 + -12 Combine like terms: 12 + -12 = 0 0 + -4v = -2 + -12 -4v = -2 + -12 Combine like terms: -2 + -12 = -14 -4v = -14 Divide each side by '-4'. v = 3.5 Simplifying v = 3.5
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