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Simplifying 2(v + -5) + 3(v + 4) = 2(v + 5) Reorder the terms: 2(-5 + v) + 3(v + 4) = 2(v + 5) (-5 * 2 + v * 2) + 3(v + 4) = 2(v + 5) (-10 + 2v) + 3(v + 4) = 2(v + 5) Reorder the terms: -10 + 2v + 3(4 + v) = 2(v + 5) -10 + 2v + (4 * 3 + v * 3) = 2(v + 5) -10 + 2v + (12 + 3v) = 2(v + 5) Reorder the terms: -10 + 12 + 2v + 3v = 2(v + 5) Combine like terms: -10 + 12 = 2 2 + 2v + 3v = 2(v + 5) Combine like terms: 2v + 3v = 5v 2 + 5v = 2(v + 5) Reorder the terms: 2 + 5v = 2(5 + v) 2 + 5v = (5 * 2 + v * 2) 2 + 5v = (10 + 2v) Solving 2 + 5v = 10 + 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. 2 + 5v + -2v = 10 + 2v + -2v Combine like terms: 5v + -2v = 3v 2 + 3v = 10 + 2v + -2v Combine like terms: 2v + -2v = 0 2 + 3v = 10 + 0 2 + 3v = 10 Add '-2' to each side of the equation. 2 + -2 + 3v = 10 + -2 Combine like terms: 2 + -2 = 0 0 + 3v = 10 + -2 3v = 10 + -2 Combine like terms: 10 + -2 = 8 3v = 8 Divide each side by '3'. v = 2.666666667 Simplifying v = 2.666666667
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