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