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Simplifying 3(v + -1) = 3v + 5 + -3(-4v + -2) Reorder the terms: 3(-1 + v) = 3v + 5 + -3(-4v + -2) (-1 * 3 + v * 3) = 3v + 5 + -3(-4v + -2) (-3 + 3v) = 3v + 5 + -3(-4v + -2) Reorder the terms: -3 + 3v = 3v + 5 + -3(-2 + -4v) -3 + 3v = 3v + 5 + (-2 * -3 + -4v * -3) -3 + 3v = 3v + 5 + (6 + 12v) Reorder the terms: -3 + 3v = 5 + 6 + 3v + 12v Combine like terms: 5 + 6 = 11 -3 + 3v = 11 + 3v + 12v Combine like terms: 3v + 12v = 15v -3 + 3v = 11 + 15v Solving -3 + 3v = 11 + 15v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-15v' to each side of the equation. -3 + 3v + -15v = 11 + 15v + -15v Combine like terms: 3v + -15v = -12v -3 + -12v = 11 + 15v + -15v Combine like terms: 15v + -15v = 0 -3 + -12v = 11 + 0 -3 + -12v = 11 Add '3' to each side of the equation. -3 + 3 + -12v = 11 + 3 Combine like terms: -3 + 3 = 0 0 + -12v = 11 + 3 -12v = 11 + 3 Combine like terms: 11 + 3 = 14 -12v = 14 Divide each side by '-12'. v = -1.166666667 Simplifying v = -1.166666667
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