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Simplifying 5(2v + -1) + 2v + 7 = 4(v + 3) + -2v Reorder the terms: 5(-1 + 2v) + 2v + 7 = 4(v + 3) + -2v (-1 * 5 + 2v * 5) + 2v + 7 = 4(v + 3) + -2v (-5 + 10v) + 2v + 7 = 4(v + 3) + -2v Reorder the terms: -5 + 7 + 10v + 2v = 4(v + 3) + -2v Combine like terms: -5 + 7 = 2 2 + 10v + 2v = 4(v + 3) + -2v Combine like terms: 10v + 2v = 12v 2 + 12v = 4(v + 3) + -2v Reorder the terms: 2 + 12v = 4(3 + v) + -2v 2 + 12v = (3 * 4 + v * 4) + -2v 2 + 12v = (12 + 4v) + -2v Combine like terms: 4v + -2v = 2v 2 + 12v = 12 + 2v Solving 2 + 12v = 12 + 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. 2 + 12v + -2v = 12 + 2v + -2v Combine like terms: 12v + -2v = 10v 2 + 10v = 12 + 2v + -2v Combine like terms: 2v + -2v = 0 2 + 10v = 12 + 0 2 + 10v = 12 Add '-2' to each side of the equation. 2 + -2 + 10v = 12 + -2 Combine like terms: 2 + -2 = 0 0 + 10v = 12 + -2 10v = 12 + -2 Combine like terms: 12 + -2 = 10 10v = 10 Divide each side by '10'. v = 1 Simplifying v = 1
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