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Simplifying 2(1 + 4v) = 8 + 7(v + -1) (1 * 2 + 4v * 2) = 8 + 7(v + -1) (2 + 8v) = 8 + 7(v + -1) Reorder the terms: 2 + 8v = 8 + 7(-1 + v) 2 + 8v = 8 + (-1 * 7 + v * 7) 2 + 8v = 8 + (-7 + 7v) Combine like terms: 8 + -7 = 1 2 + 8v = 1 + 7v Solving 2 + 8v = 1 + 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. 2 + 8v + -7v = 1 + 7v + -7v Combine like terms: 8v + -7v = 1v 2 + 1v = 1 + 7v + -7v Combine like terms: 7v + -7v = 0 2 + 1v = 1 + 0 2 + 1v = 1 Add '-2' to each side of the equation. 2 + -2 + 1v = 1 + -2 Combine like terms: 2 + -2 = 0 0 + 1v = 1 + -2 1v = 1 + -2 Combine like terms: 1 + -2 = -1 1v = -1 Divide each side by '1'. v = -1 Simplifying v = -1
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