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Simplifying 3(2v + -1) + 4v + 7 = 4(v + -1) + 2v Reorder the terms: 3(-1 + 2v) + 4v + 7 = 4(v + -1) + 2v (-1 * 3 + 2v * 3) + 4v + 7 = 4(v + -1) + 2v (-3 + 6v) + 4v + 7 = 4(v + -1) + 2v Reorder the terms: -3 + 7 + 6v + 4v = 4(v + -1) + 2v Combine like terms: -3 + 7 = 4 4 + 6v + 4v = 4(v + -1) + 2v Combine like terms: 6v + 4v = 10v 4 + 10v = 4(v + -1) + 2v Reorder the terms: 4 + 10v = 4(-1 + v) + 2v 4 + 10v = (-1 * 4 + v * 4) + 2v 4 + 10v = (-4 + 4v) + 2v Combine like terms: 4v + 2v = 6v 4 + 10v = -4 + 6v Solving 4 + 10v = -4 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. 4 + 10v + -6v = -4 + 6v + -6v Combine like terms: 10v + -6v = 4v 4 + 4v = -4 + 6v + -6v Combine like terms: 6v + -6v = 0 4 + 4v = -4 + 0 4 + 4v = -4 Add '-4' to each side of the equation. 4 + -4 + 4v = -4 + -4 Combine like terms: 4 + -4 = 0 0 + 4v = -4 + -4 4v = -4 + -4 Combine like terms: -4 + -4 = -8 4v = -8 Divide each side by '4'. v = -2 Simplifying v = -2
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