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Simplifying v + -2w + 39 = 3v + w + -8 Reorder the terms: 39 + v + -2w = 3v + w + -8 Reorder the terms: 39 + v + -2w = -8 + 3v + w Solving 39 + v + -2w = -8 + 3v + w 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. 39 + v + -3v + -2w = -8 + 3v + -3v + w Combine like terms: v + -3v = -2v 39 + -2v + -2w = -8 + 3v + -3v + w Combine like terms: 3v + -3v = 0 39 + -2v + -2w = -8 + 0 + w 39 + -2v + -2w = -8 + w Add '-39' to each side of the equation. 39 + -2v + -39 + -2w = -8 + -39 + w Reorder the terms: 39 + -39 + -2v + -2w = -8 + -39 + w Combine like terms: 39 + -39 = 0 0 + -2v + -2w = -8 + -39 + w -2v + -2w = -8 + -39 + w Combine like terms: -8 + -39 = -47 -2v + -2w = -47 + w Add '2w' to each side of the equation. -2v + -2w + 2w = -47 + w + 2w Combine like terms: -2w + 2w = 0 -2v + 0 = -47 + w + 2w -2v = -47 + w + 2w Combine like terms: w + 2w = 3w -2v = -47 + 3w Divide each side by '-2'. v = 23.5 + -1.5w Simplifying v = 23.5 + -1.5w
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