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Simplifying 3v + -7 + 2(3v + 2) = -3(v + 4) Reorder the terms: 3v + -7 + 2(2 + 3v) = -3(v + 4) 3v + -7 + (2 * 2 + 3v * 2) = -3(v + 4) 3v + -7 + (4 + 6v) = -3(v + 4) Reorder the terms: -7 + 4 + 3v + 6v = -3(v + 4) Combine like terms: -7 + 4 = -3 -3 + 3v + 6v = -3(v + 4) Combine like terms: 3v + 6v = 9v -3 + 9v = -3(v + 4) Reorder the terms: -3 + 9v = -3(4 + v) -3 + 9v = (4 * -3 + v * -3) -3 + 9v = (-12 + -3v) Solving -3 + 9v = -12 + -3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3v' to each side of the equation. -3 + 9v + 3v = -12 + -3v + 3v Combine like terms: 9v + 3v = 12v -3 + 12v = -12 + -3v + 3v Combine like terms: -3v + 3v = 0 -3 + 12v = -12 + 0 -3 + 12v = -12 Add '3' to each side of the equation. -3 + 3 + 12v = -12 + 3 Combine like terms: -3 + 3 = 0 0 + 12v = -12 + 3 12v = -12 + 3 Combine like terms: -12 + 3 = -9 12v = -9 Divide each side by '12'. v = -0.75 Simplifying v = -0.75
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