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Simplifying 3(4v + 1) + -3(2v + 3) + -2(v + -7) = w Reorder the terms: 3(1 + 4v) + -3(2v + 3) + -2(v + -7) = w (1 * 3 + 4v * 3) + -3(2v + 3) + -2(v + -7) = w (3 + 12v) + -3(2v + 3) + -2(v + -7) = w Reorder the terms: 3 + 12v + -3(3 + 2v) + -2(v + -7) = w 3 + 12v + (3 * -3 + 2v * -3) + -2(v + -7) = w 3 + 12v + (-9 + -6v) + -2(v + -7) = w Reorder the terms: 3 + 12v + -9 + -6v + -2(-7 + v) = w 3 + 12v + -9 + -6v + (-7 * -2 + v * -2) = w 3 + 12v + -9 + -6v + (14 + -2v) = w Reorder the terms: 3 + -9 + 14 + 12v + -6v + -2v = w Combine like terms: 3 + -9 = -6 -6 + 14 + 12v + -6v + -2v = w Combine like terms: -6 + 14 = 8 8 + 12v + -6v + -2v = w Combine like terms: 12v + -6v = 6v 8 + 6v + -2v = w Combine like terms: 6v + -2v = 4v 8 + 4v = w Solving 8 + 4v = w Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 4v = -8 + w Combine like terms: 8 + -8 = 0 0 + 4v = -8 + w 4v = -8 + w Divide each side by '4'. v = -2 + 0.25w Simplifying v = -2 + 0.25w
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