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Simplifying 5v + -9 + 3(3v + 1) = -2(v + 6) Reorder the terms: 5v + -9 + 3(1 + 3v) = -2(v + 6) 5v + -9 + (1 * 3 + 3v * 3) = -2(v + 6) 5v + -9 + (3 + 9v) = -2(v + 6) Reorder the terms: -9 + 3 + 5v + 9v = -2(v + 6) Combine like terms: -9 + 3 = -6 -6 + 5v + 9v = -2(v + 6) Combine like terms: 5v + 9v = 14v -6 + 14v = -2(v + 6) Reorder the terms: -6 + 14v = -2(6 + v) -6 + 14v = (6 * -2 + v * -2) -6 + 14v = (-12 + -2v) Solving -6 + 14v = -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. -6 + 14v + 2v = -12 + -2v + 2v Combine like terms: 14v + 2v = 16v -6 + 16v = -12 + -2v + 2v Combine like terms: -2v + 2v = 0 -6 + 16v = -12 + 0 -6 + 16v = -12 Add '6' to each side of the equation. -6 + 6 + 16v = -12 + 6 Combine like terms: -6 + 6 = 0 0 + 16v = -12 + 6 16v = -12 + 6 Combine like terms: -12 + 6 = -6 16v = -6 Divide each side by '16'. v = -0.375 Simplifying v = -0.375
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