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Simplifying 6(3v + 2) + -3(4v + 5) = 4(v + -6) + w Reorder the terms: 6(2 + 3v) + -3(4v + 5) = 4(v + -6) + w (2 * 6 + 3v * 6) + -3(4v + 5) = 4(v + -6) + w (12 + 18v) + -3(4v + 5) = 4(v + -6) + w Reorder the terms: 12 + 18v + -3(5 + 4v) = 4(v + -6) + w 12 + 18v + (5 * -3 + 4v * -3) = 4(v + -6) + w 12 + 18v + (-15 + -12v) = 4(v + -6) + w Reorder the terms: 12 + -15 + 18v + -12v = 4(v + -6) + w Combine like terms: 12 + -15 = -3 -3 + 18v + -12v = 4(v + -6) + w Combine like terms: 18v + -12v = 6v -3 + 6v = 4(v + -6) + w Reorder the terms: -3 + 6v = 4(-6 + v) + w -3 + 6v = (-6 * 4 + v * 4) + w -3 + 6v = (-24 + 4v) + w Solving -3 + 6v = -24 + 4v + w Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4v' to each side of the equation. -3 + 6v + -4v = -24 + 4v + -4v + w Combine like terms: 6v + -4v = 2v -3 + 2v = -24 + 4v + -4v + w Combine like terms: 4v + -4v = 0 -3 + 2v = -24 + 0 + w -3 + 2v = -24 + w Add '3' to each side of the equation. -3 + 3 + 2v = -24 + 3 + w Combine like terms: -3 + 3 = 0 0 + 2v = -24 + 3 + w 2v = -24 + 3 + w Combine like terms: -24 + 3 = -21 2v = -21 + w Divide each side by '2'. v = -10.5 + 0.5w Simplifying v = -10.5 + 0.5w
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