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Simplifying 3(2v + 8w) + 4(2v + 4w) = 0 (2v * 3 + 8w * 3) + 4(2v + 4w) = 0 (6v + 24w) + 4(2v + 4w) = 0 6v + 24w + (2v * 4 + 4w * 4) = 0 6v + 24w + (8v + 16w) = 0 Reorder the terms: 6v + 8v + 24w + 16w = 0 Combine like terms: 6v + 8v = 14v 14v + 24w + 16w = 0 Combine like terms: 24w + 16w = 40w 14v + 40w = 0 Solving 14v + 40w = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-40w' to each side of the equation. 14v + 40w + -40w = 0 + -40w Combine like terms: 40w + -40w = 0 14v + 0 = 0 + -40w 14v = 0 + -40w Remove the zero: 14v = -40w Divide each side by '14'. v = -2.857142857w Simplifying v = -2.857142857w
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