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Simplifying -2(3v + -9) + 5v = 9 + 2(4v + -3) Reorder the terms: -2(-9 + 3v) + 5v = 9 + 2(4v + -3) (-9 * -2 + 3v * -2) + 5v = 9 + 2(4v + -3) (18 + -6v) + 5v = 9 + 2(4v + -3) Combine like terms: -6v + 5v = -1v 18 + -1v = 9 + 2(4v + -3) Reorder the terms: 18 + -1v = 9 + 2(-3 + 4v) 18 + -1v = 9 + (-3 * 2 + 4v * 2) 18 + -1v = 9 + (-6 + 8v) Combine like terms: 9 + -6 = 3 18 + -1v = 3 + 8v Solving 18 + -1v = 3 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. 18 + -1v + -8v = 3 + 8v + -8v Combine like terms: -1v + -8v = -9v 18 + -9v = 3 + 8v + -8v Combine like terms: 8v + -8v = 0 18 + -9v = 3 + 0 18 + -9v = 3 Add '-18' to each side of the equation. 18 + -18 + -9v = 3 + -18 Combine like terms: 18 + -18 = 0 0 + -9v = 3 + -18 -9v = 3 + -18 Combine like terms: 3 + -18 = -15 -9v = -15 Divide each side by '-9'. v = 1.666666667 Simplifying v = 1.666666667
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