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Simplifying -3(1 + 9v) = 3v + 3(1 + -12v) (1 * -3 + 9v * -3) = 3v + 3(1 + -12v) (-3 + -27v) = 3v + 3(1 + -12v) -3 + -27v = 3v + (1 * 3 + -12v * 3) -3 + -27v = 3v + (3 + -36v) Reorder the terms: -3 + -27v = 3 + 3v + -36v Combine like terms: 3v + -36v = -33v -3 + -27v = 3 + -33v Solving -3 + -27v = 3 + -33v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '33v' to each side of the equation. -3 + -27v + 33v = 3 + -33v + 33v Combine like terms: -27v + 33v = 6v -3 + 6v = 3 + -33v + 33v Combine like terms: -33v + 33v = 0 -3 + 6v = 3 + 0 -3 + 6v = 3 Add '3' to each side of the equation. -3 + 3 + 6v = 3 + 3 Combine like terms: -3 + 3 = 0 0 + 6v = 3 + 3 6v = 3 + 3 Combine like terms: 3 + 3 = 6 6v = 6 Divide each side by '6'. v = 1 Simplifying v = 1
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