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Simplifying -5(8v + -5) + 2(v + 7) = 4v + -1 + -2 Reorder the terms: -5(-5 + 8v) + 2(v + 7) = 4v + -1 + -2 (-5 * -5 + 8v * -5) + 2(v + 7) = 4v + -1 + -2 (25 + -40v) + 2(v + 7) = 4v + -1 + -2 Reorder the terms: 25 + -40v + 2(7 + v) = 4v + -1 + -2 25 + -40v + (7 * 2 + v * 2) = 4v + -1 + -2 25 + -40v + (14 + 2v) = 4v + -1 + -2 Reorder the terms: 25 + 14 + -40v + 2v = 4v + -1 + -2 Combine like terms: 25 + 14 = 39 39 + -40v + 2v = 4v + -1 + -2 Combine like terms: -40v + 2v = -38v 39 + -38v = 4v + -1 + -2 Reorder the terms: 39 + -38v = -1 + -2 + 4v Combine like terms: -1 + -2 = -3 39 + -38v = -3 + 4v Solving 39 + -38v = -3 + 4v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4v' to each side of the equation. 39 + -38v + -4v = -3 + 4v + -4v Combine like terms: -38v + -4v = -42v 39 + -42v = -3 + 4v + -4v Combine like terms: 4v + -4v = 0 39 + -42v = -3 + 0 39 + -42v = -3 Add '-39' to each side of the equation. 39 + -39 + -42v = -3 + -39 Combine like terms: 39 + -39 = 0 0 + -42v = -3 + -39 -42v = -3 + -39 Combine like terms: -3 + -39 = -42 -42v = -42 Divide each side by '-42'. v = 1 Simplifying v = 1
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