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Simplifying 2(3v + -3) + -1(v + 4) + -3(v + -1) = -15 Reorder the terms: 2(-3 + 3v) + -1(v + 4) + -3(v + -1) = -15 (-3 * 2 + 3v * 2) + -1(v + 4) + -3(v + -1) = -15 (-6 + 6v) + -1(v + 4) + -3(v + -1) = -15 Reorder the terms: -6 + 6v + -1(4 + v) + -3(v + -1) = -15 -6 + 6v + (4 * -1 + v * -1) + -3(v + -1) = -15 -6 + 6v + (-4 + -1v) + -3(v + -1) = -15 Reorder the terms: -6 + 6v + -4 + -1v + -3(-1 + v) = -15 -6 + 6v + -4 + -1v + (-1 * -3 + v * -3) = -15 -6 + 6v + -4 + -1v + (3 + -3v) = -15 Reorder the terms: -6 + -4 + 3 + 6v + -1v + -3v = -15 Combine like terms: -6 + -4 = -10 -10 + 3 + 6v + -1v + -3v = -15 Combine like terms: -10 + 3 = -7 -7 + 6v + -1v + -3v = -15 Combine like terms: 6v + -1v = 5v -7 + 5v + -3v = -15 Combine like terms: 5v + -3v = 2v -7 + 2v = -15 Solving -7 + 2v = -15 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2v = -15 + 7 Combine like terms: -7 + 7 = 0 0 + 2v = -15 + 7 2v = -15 + 7 Combine like terms: -15 + 7 = -8 2v = -8 Divide each side by '2'. v = -4 Simplifying v = -4
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