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Simplifying 3(3v + -2) + 7v = 6(v + 6) + 4v Reorder the terms: 3(-2 + 3v) + 7v = 6(v + 6) + 4v (-2 * 3 + 3v * 3) + 7v = 6(v + 6) + 4v (-6 + 9v) + 7v = 6(v + 6) + 4v Combine like terms: 9v + 7v = 16v -6 + 16v = 6(v + 6) + 4v Reorder the terms: -6 + 16v = 6(6 + v) + 4v -6 + 16v = (6 * 6 + v * 6) + 4v -6 + 16v = (36 + 6v) + 4v Combine like terms: 6v + 4v = 10v -6 + 16v = 36 + 10v Solving -6 + 16v = 36 + 10v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10v' to each side of the equation. -6 + 16v + -10v = 36 + 10v + -10v Combine like terms: 16v + -10v = 6v -6 + 6v = 36 + 10v + -10v Combine like terms: 10v + -10v = 0 -6 + 6v = 36 + 0 -6 + 6v = 36 Add '6' to each side of the equation. -6 + 6 + 6v = 36 + 6 Combine like terms: -6 + 6 = 0 0 + 6v = 36 + 6 6v = 36 + 6 Combine like terms: 36 + 6 = 42 6v = 42 Divide each side by '6'. v = 7 Simplifying v = 7
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