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Simplifying 7(v + 5) = 56(v + 7) Reorder the terms: 7(5 + v) = 56(v + 7) (5 * 7 + v * 7) = 56(v + 7) (35 + 7v) = 56(v + 7) Reorder the terms: 35 + 7v = 56(7 + v) 35 + 7v = (7 * 56 + v * 56) 35 + 7v = (392 + 56v) Solving 35 + 7v = 392 + 56v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-56v' to each side of the equation. 35 + 7v + -56v = 392 + 56v + -56v Combine like terms: 7v + -56v = -49v 35 + -49v = 392 + 56v + -56v Combine like terms: 56v + -56v = 0 35 + -49v = 392 + 0 35 + -49v = 392 Add '-35' to each side of the equation. 35 + -35 + -49v = 392 + -35 Combine like terms: 35 + -35 = 0 0 + -49v = 392 + -35 -49v = 392 + -35 Combine like terms: 392 + -35 = 357 -49v = 357 Divide each side by '-49'. v = -7.285714286 Simplifying v = -7.285714286
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