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Simplifying 6(7 + v) = -2(v + 7) (7 * 6 + v * 6) = -2(v + 7) (42 + 6v) = -2(v + 7) Reorder the terms: 42 + 6v = -2(7 + v) 42 + 6v = (7 * -2 + v * -2) 42 + 6v = (-14 + -2v) Solving 42 + 6v = -14 + -2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2v' to each side of the equation. 42 + 6v + 2v = -14 + -2v + 2v Combine like terms: 6v + 2v = 8v 42 + 8v = -14 + -2v + 2v Combine like terms: -2v + 2v = 0 42 + 8v = -14 + 0 42 + 8v = -14 Add '-42' to each side of the equation. 42 + -42 + 8v = -14 + -42 Combine like terms: 42 + -42 = 0 0 + 8v = -14 + -42 8v = -14 + -42 Combine like terms: -14 + -42 = -56 8v = -56 Divide each side by '8'. v = -7 Simplifying v = -7
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