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Simplifying -3(2v + 9) + -3(3v + -7) = 4v + 6(2v + -8) Reorder the terms: -3(9 + 2v) + -3(3v + -7) = 4v + 6(2v + -8) (9 * -3 + 2v * -3) + -3(3v + -7) = 4v + 6(2v + -8) (-27 + -6v) + -3(3v + -7) = 4v + 6(2v + -8) Reorder the terms: -27 + -6v + -3(-7 + 3v) = 4v + 6(2v + -8) -27 + -6v + (-7 * -3 + 3v * -3) = 4v + 6(2v + -8) -27 + -6v + (21 + -9v) = 4v + 6(2v + -8) Reorder the terms: -27 + 21 + -6v + -9v = 4v + 6(2v + -8) Combine like terms: -27 + 21 = -6 -6 + -6v + -9v = 4v + 6(2v + -8) Combine like terms: -6v + -9v = -15v -6 + -15v = 4v + 6(2v + -8) Reorder the terms: -6 + -15v = 4v + 6(-8 + 2v) -6 + -15v = 4v + (-8 * 6 + 2v * 6) -6 + -15v = 4v + (-48 + 12v) Reorder the terms: -6 + -15v = -48 + 4v + 12v Combine like terms: 4v + 12v = 16v -6 + -15v = -48 + 16v Solving -6 + -15v = -48 + 16v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-16v' to each side of the equation. -6 + -15v + -16v = -48 + 16v + -16v Combine like terms: -15v + -16v = -31v -6 + -31v = -48 + 16v + -16v Combine like terms: 16v + -16v = 0 -6 + -31v = -48 + 0 -6 + -31v = -48 Add '6' to each side of the equation. -6 + 6 + -31v = -48 + 6 Combine like terms: -6 + 6 = 0 0 + -31v = -48 + 6 -31v = -48 + 6 Combine like terms: -48 + 6 = -42 -31v = -42 Divide each side by '-31'. v = 1.35483871 Simplifying v = 1.35483871
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