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Simplifying 1 + 3(5v + -3) = -3(2v + -2) + 9v Reorder the terms: 1 + 3(-3 + 5v) = -3(2v + -2) + 9v 1 + (-3 * 3 + 5v * 3) = -3(2v + -2) + 9v 1 + (-9 + 15v) = -3(2v + -2) + 9v Combine like terms: 1 + -9 = -8 -8 + 15v = -3(2v + -2) + 9v Reorder the terms: -8 + 15v = -3(-2 + 2v) + 9v -8 + 15v = (-2 * -3 + 2v * -3) + 9v -8 + 15v = (6 + -6v) + 9v Combine like terms: -6v + 9v = 3v -8 + 15v = 6 + 3v Solving -8 + 15v = 6 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. -8 + 15v + -3v = 6 + 3v + -3v Combine like terms: 15v + -3v = 12v -8 + 12v = 6 + 3v + -3v Combine like terms: 3v + -3v = 0 -8 + 12v = 6 + 0 -8 + 12v = 6 Add '8' to each side of the equation. -8 + 8 + 12v = 6 + 8 Combine like terms: -8 + 8 = 0 0 + 12v = 6 + 8 12v = 6 + 8 Combine like terms: 6 + 8 = 14 12v = 14 Divide each side by '12'. v = 1.166666667 Simplifying v = 1.166666667
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