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Simplifying 3(4v + 1) + -3(2v + 3) = (2v + -7) + w Reorder the terms: 3(1 + 4v) + -3(2v + 3) = (2v + -7) + w (1 * 3 + 4v * 3) + -3(2v + 3) = (2v + -7) + w (3 + 12v) + -3(2v + 3) = (2v + -7) + w Reorder the terms: 3 + 12v + -3(3 + 2v) = (2v + -7) + w 3 + 12v + (3 * -3 + 2v * -3) = (2v + -7) + w 3 + 12v + (-9 + -6v) = (2v + -7) + w Reorder the terms: 3 + -9 + 12v + -6v = (2v + -7) + w Combine like terms: 3 + -9 = -6 -6 + 12v + -6v = (2v + -7) + w Combine like terms: 12v + -6v = 6v -6 + 6v = (2v + -7) + w Reorder the terms: -6 + 6v = (-7 + 2v) + w Remove parenthesis around (-7 + 2v) -6 + 6v = -7 + 2v + w Solving -6 + 6v = -7 + 2v + w Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2v' to each side of the equation. -6 + 6v + -2v = -7 + 2v + -2v + w Combine like terms: 6v + -2v = 4v -6 + 4v = -7 + 2v + -2v + w Combine like terms: 2v + -2v = 0 -6 + 4v = -7 + 0 + w -6 + 4v = -7 + w Add '6' to each side of the equation. -6 + 6 + 4v = -7 + 6 + w Combine like terms: -6 + 6 = 0 0 + 4v = -7 + 6 + w 4v = -7 + 6 + w Combine like terms: -7 + 6 = -1 4v = -1 + w Divide each side by '4'. v = -0.25 + 0.25w Simplifying v = -0.25 + 0.25w
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