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