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Simplifying -3(v + 1) = 3v + -3 + 3(2v + 6) Reorder the terms: -3(1 + v) = 3v + -3 + 3(2v + 6) (1 * -3 + v * -3) = 3v + -3 + 3(2v + 6) (-3 + -3v) = 3v + -3 + 3(2v + 6) Reorder the terms: -3 + -3v = 3v + -3 + 3(6 + 2v) -3 + -3v = 3v + -3 + (6 * 3 + 2v * 3) -3 + -3v = 3v + -3 + (18 + 6v) Reorder the terms: -3 + -3v = -3 + 18 + 3v + 6v Combine like terms: -3 + 18 = 15 -3 + -3v = 15 + 3v + 6v Combine like terms: 3v + 6v = 9v -3 + -3v = 15 + 9v Solving -3 + -3v = 15 + 9v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9v' to each side of the equation. -3 + -3v + -9v = 15 + 9v + -9v Combine like terms: -3v + -9v = -12v -3 + -12v = 15 + 9v + -9v Combine like terms: 9v + -9v = 0 -3 + -12v = 15 + 0 -3 + -12v = 15 Add '3' to each side of the equation. -3 + 3 + -12v = 15 + 3 Combine like terms: -3 + 3 = 0 0 + -12v = 15 + 3 -12v = 15 + 3 Combine like terms: 15 + 3 = 18 -12v = 18 Divide each side by '-12'. v = -1.5 Simplifying v = -1.5
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