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Simplifying -7(v + 2) + 2v + 6 = 5v + 12 Reorder the terms: -7(2 + v) + 2v + 6 = 5v + 12 (2 * -7 + v * -7) + 2v + 6 = 5v + 12 (-14 + -7v) + 2v + 6 = 5v + 12 Reorder the terms: -14 + 6 + -7v + 2v = 5v + 12 Combine like terms: -14 + 6 = -8 -8 + -7v + 2v = 5v + 12 Combine like terms: -7v + 2v = -5v -8 + -5v = 5v + 12 Reorder the terms: -8 + -5v = 12 + 5v Solving -8 + -5v = 12 + 5v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5v' to each side of the equation. -8 + -5v + -5v = 12 + 5v + -5v Combine like terms: -5v + -5v = -10v -8 + -10v = 12 + 5v + -5v Combine like terms: 5v + -5v = 0 -8 + -10v = 12 + 0 -8 + -10v = 12 Add '8' to each side of the equation. -8 + 8 + -10v = 12 + 8 Combine like terms: -8 + 8 = 0 0 + -10v = 12 + 8 -10v = 12 + 8 Combine like terms: 12 + 8 = 20 -10v = 20 Divide each side by '-10'. v = -2 Simplifying v = -2
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