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Simplifying 3v + 27 = -7(1 + -5v) + 2 Reorder the terms: 27 + 3v = -7(1 + -5v) + 2 27 + 3v = (1 * -7 + -5v * -7) + 2 27 + 3v = (-7 + 35v) + 2 Reorder the terms: 27 + 3v = -7 + 2 + 35v Combine like terms: -7 + 2 = -5 27 + 3v = -5 + 35v Solving 27 + 3v = -5 + 35v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-35v' to each side of the equation. 27 + 3v + -35v = -5 + 35v + -35v Combine like terms: 3v + -35v = -32v 27 + -32v = -5 + 35v + -35v Combine like terms: 35v + -35v = 0 27 + -32v = -5 + 0 27 + -32v = -5 Add '-27' to each side of the equation. 27 + -27 + -32v = -5 + -27 Combine like terms: 27 + -27 = 0 0 + -32v = -5 + -27 -32v = -5 + -27 Combine like terms: -5 + -27 = -32 -32v = -32 Divide each side by '-32'. v = 1 Simplifying v = 1
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