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Simplifying 5(v + -5) + 3(v + 2) = -4v + 7 + 3v + -8 Reorder the terms: 5(-5 + v) + 3(v + 2) = -4v + 7 + 3v + -8 (-5 * 5 + v * 5) + 3(v + 2) = -4v + 7 + 3v + -8 (-25 + 5v) + 3(v + 2) = -4v + 7 + 3v + -8 Reorder the terms: -25 + 5v + 3(2 + v) = -4v + 7 + 3v + -8 -25 + 5v + (2 * 3 + v * 3) = -4v + 7 + 3v + -8 -25 + 5v + (6 + 3v) = -4v + 7 + 3v + -8 Reorder the terms: -25 + 6 + 5v + 3v = -4v + 7 + 3v + -8 Combine like terms: -25 + 6 = -19 -19 + 5v + 3v = -4v + 7 + 3v + -8 Combine like terms: 5v + 3v = 8v -19 + 8v = -4v + 7 + 3v + -8 Reorder the terms: -19 + 8v = 7 + -8 + -4v + 3v Combine like terms: 7 + -8 = -1 -19 + 8v = -1 + -4v + 3v Combine like terms: -4v + 3v = -1v -19 + 8v = -1 + -1v Solving -19 + 8v = -1 + -1v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add 'v' to each side of the equation. -19 + 8v + v = -1 + -1v + v Combine like terms: 8v + v = 9v -19 + 9v = -1 + -1v + v Combine like terms: -1v + v = 0 -19 + 9v = -1 + 0 -19 + 9v = -1 Add '19' to each side of the equation. -19 + 19 + 9v = -1 + 19 Combine like terms: -19 + 19 = 0 0 + 9v = -1 + 19 9v = -1 + 19 Combine like terms: -1 + 19 = 18 9v = 18 Divide each side by '9'. v = 2 Simplifying v = 2
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