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Simplifying 2(2v + -1) + 6v = 2 + 3(4v + -2) Reorder the terms: 2(-1 + 2v) + 6v = 2 + 3(4v + -2) (-1 * 2 + 2v * 2) + 6v = 2 + 3(4v + -2) (-2 + 4v) + 6v = 2 + 3(4v + -2) Combine like terms: 4v + 6v = 10v -2 + 10v = 2 + 3(4v + -2) Reorder the terms: -2 + 10v = 2 + 3(-2 + 4v) -2 + 10v = 2 + (-2 * 3 + 4v * 3) -2 + 10v = 2 + (-6 + 12v) Combine like terms: 2 + -6 = -4 -2 + 10v = -4 + 12v Solving -2 + 10v = -4 + 12v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12v' to each side of the equation. -2 + 10v + -12v = -4 + 12v + -12v Combine like terms: 10v + -12v = -2v -2 + -2v = -4 + 12v + -12v Combine like terms: 12v + -12v = 0 -2 + -2v = -4 + 0 -2 + -2v = -4 Add '2' to each side of the equation. -2 + 2 + -2v = -4 + 2 Combine like terms: -2 + 2 = 0 0 + -2v = -4 + 2 -2v = -4 + 2 Combine like terms: -4 + 2 = -2 -2v = -2 Divide each side by '-2'. v = 1 Simplifying v = 1
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