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Simplifying 46(v + -80) + 14(v + -39) = v + -52 + v + 60 Reorder the terms: 46(-80 + v) + 14(v + -39) = v + -52 + v + 60 (-80 * 46 + v * 46) + 14(v + -39) = v + -52 + v + 60 (-3680 + 46v) + 14(v + -39) = v + -52 + v + 60 Reorder the terms: -3680 + 46v + 14(-39 + v) = v + -52 + v + 60 -3680 + 46v + (-39 * 14 + v * 14) = v + -52 + v + 60 -3680 + 46v + (-546 + 14v) = v + -52 + v + 60 Reorder the terms: -3680 + -546 + 46v + 14v = v + -52 + v + 60 Combine like terms: -3680 + -546 = -4226 -4226 + 46v + 14v = v + -52 + v + 60 Combine like terms: 46v + 14v = 60v -4226 + 60v = v + -52 + v + 60 Reorder the terms: -4226 + 60v = -52 + 60 + v + v Combine like terms: -52 + 60 = 8 -4226 + 60v = 8 + v + v Combine like terms: v + v = 2v -4226 + 60v = 8 + 2v Solving -4226 + 60v = 8 + 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. -4226 + 60v + -2v = 8 + 2v + -2v Combine like terms: 60v + -2v = 58v -4226 + 58v = 8 + 2v + -2v Combine like terms: 2v + -2v = 0 -4226 + 58v = 8 + 0 -4226 + 58v = 8 Add '4226' to each side of the equation. -4226 + 4226 + 58v = 8 + 4226 Combine like terms: -4226 + 4226 = 0 0 + 58v = 8 + 4226 58v = 8 + 4226 Combine like terms: 8 + 4226 = 4234 58v = 4234 Divide each side by '58'. v = 73 Simplifying v = 73
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