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Simplifying -2(2v + -6) + 7v = 7(v + 2) Reorder the terms: -2(-6 + 2v) + 7v = 7(v + 2) (-6 * -2 + 2v * -2) + 7v = 7(v + 2) (12 + -4v) + 7v = 7(v + 2) Combine like terms: -4v + 7v = 3v 12 + 3v = 7(v + 2) Reorder the terms: 12 + 3v = 7(2 + v) 12 + 3v = (2 * 7 + v * 7) 12 + 3v = (14 + 7v) Solving 12 + 3v = 14 + 7v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7v' to each side of the equation. 12 + 3v + -7v = 14 + 7v + -7v Combine like terms: 3v + -7v = -4v 12 + -4v = 14 + 7v + -7v Combine like terms: 7v + -7v = 0 12 + -4v = 14 + 0 12 + -4v = 14 Add '-12' to each side of the equation. 12 + -12 + -4v = 14 + -12 Combine like terms: 12 + -12 = 0 0 + -4v = 14 + -12 -4v = 14 + -12 Combine like terms: 14 + -12 = 2 -4v = 2 Divide each side by '-4'. v = -0.5 Simplifying v = -0.5
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