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Simplifying 3v + -6 + 9(4v + -8) = 8 + -1(2v + -6) + 4 Reorder the terms: 3v + -6 + 9(-8 + 4v) = 8 + -1(2v + -6) + 4 3v + -6 + (-8 * 9 + 4v * 9) = 8 + -1(2v + -6) + 4 3v + -6 + (-72 + 36v) = 8 + -1(2v + -6) + 4 Reorder the terms: -6 + -72 + 3v + 36v = 8 + -1(2v + -6) + 4 Combine like terms: -6 + -72 = -78 -78 + 3v + 36v = 8 + -1(2v + -6) + 4 Combine like terms: 3v + 36v = 39v -78 + 39v = 8 + -1(2v + -6) + 4 Reorder the terms: -78 + 39v = 8 + -1(-6 + 2v) + 4 -78 + 39v = 8 + (-6 * -1 + 2v * -1) + 4 -78 + 39v = 8 + (6 + -2v) + 4 Reorder the terms: -78 + 39v = 8 + 6 + 4 + -2v Combine like terms: 8 + 6 = 14 -78 + 39v = 14 + 4 + -2v Combine like terms: 14 + 4 = 18 -78 + 39v = 18 + -2v Solving -78 + 39v = 18 + -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. -78 + 39v + 2v = 18 + -2v + 2v Combine like terms: 39v + 2v = 41v -78 + 41v = 18 + -2v + 2v Combine like terms: -2v + 2v = 0 -78 + 41v = 18 + 0 -78 + 41v = 18 Add '78' to each side of the equation. -78 + 78 + 41v = 18 + 78 Combine like terms: -78 + 78 = 0 0 + 41v = 18 + 78 41v = 18 + 78 Combine like terms: 18 + 78 = 96 41v = 96 Divide each side by '41'. v = 2.341463415 Simplifying v = 2.341463415
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