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Simplifying -5(-5 + -3v) + -7(v + 7) = -1v + 7v (-5 * -5 + -3v * -5) + -7(v + 7) = -1v + 7v (25 + 15v) + -7(v + 7) = -1v + 7v Reorder the terms: 25 + 15v + -7(7 + v) = -1v + 7v 25 + 15v + (7 * -7 + v * -7) = -1v + 7v 25 + 15v + (-49 + -7v) = -1v + 7v Reorder the terms: 25 + -49 + 15v + -7v = -1v + 7v Combine like terms: 25 + -49 = -24 -24 + 15v + -7v = -1v + 7v Combine like terms: 15v + -7v = 8v -24 + 8v = -1v + 7v Combine like terms: -1v + 7v = 6v -24 + 8v = 6v Solving -24 + 8v = 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. -24 + 8v + -6v = 6v + -6v Combine like terms: 8v + -6v = 2v -24 + 2v = 6v + -6v Combine like terms: 6v + -6v = 0 -24 + 2v = 0 Add '24' to each side of the equation. -24 + 24 + 2v = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 2v = 0 + 24 2v = 0 + 24 Combine like terms: 0 + 24 = 24 2v = 24 Divide each side by '2'. v = 12 Simplifying v = 12
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