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Simplifying 2v + -2v = -2(4v + 7) + 6(2v + -3) Combine like terms: 2v + -2v = 0 0 = -2(4v + 7) + 6(2v + -3) Reorder the terms: 0 = -2(7 + 4v) + 6(2v + -3) 0 = (7 * -2 + 4v * -2) + 6(2v + -3) 0 = (-14 + -8v) + 6(2v + -3) Reorder the terms: 0 = -14 + -8v + 6(-3 + 2v) 0 = -14 + -8v + (-3 * 6 + 2v * 6) 0 = -14 + -8v + (-18 + 12v) Reorder the terms: 0 = -14 + -18 + -8v + 12v Combine like terms: -14 + -18 = -32 0 = -32 + -8v + 12v Combine like terms: -8v + 12v = 4v 0 = -32 + 4v Solving 0 = -32 + 4v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4v' to each side of the equation. 0 + -4v = -32 + 4v + -4v Remove the zero: -4v = -32 + 4v + -4v Combine like terms: 4v + -4v = 0 -4v = -32 + 0 -4v = -32 Divide each side by '-4'. v = 8 Simplifying v = 8
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