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Simplifying 9(v + -2) = 2v + 31 Reorder the terms: 9(-2 + v) = 2v + 31 (-2 * 9 + v * 9) = 2v + 31 (-18 + 9v) = 2v + 31 Reorder the terms: -18 + 9v = 31 + 2v Solving -18 + 9v = 31 + 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. -18 + 9v + -2v = 31 + 2v + -2v Combine like terms: 9v + -2v = 7v -18 + 7v = 31 + 2v + -2v Combine like terms: 2v + -2v = 0 -18 + 7v = 31 + 0 -18 + 7v = 31 Add '18' to each side of the equation. -18 + 18 + 7v = 31 + 18 Combine like terms: -18 + 18 = 0 0 + 7v = 31 + 18 7v = 31 + 18 Combine like terms: 31 + 18 = 49 7v = 49 Divide each side by '7'. v = 7 Simplifying v = 7
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