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Simplifying 0.8(3v + -2w) + 0.2(7v + -2w) = 0 (3v * 0.8 + -2w * 0.8) + 0.2(7v + -2w) = 0 (2.4v + -1.6w) + 0.2(7v + -2w) = 0 2.4v + -1.6w + (7v * 0.2 + -2w * 0.2) = 0 2.4v + -1.6w + (1.4v + -0.4w) = 0 Reorder the terms: 2.4v + 1.4v + -1.6w + -0.4w = 0 Combine like terms: 2.4v + 1.4v = 3.8v 3.8v + -1.6w + -0.4w = 0 Combine like terms: -1.6w + -0.4w = -2w 3.8v + -2w = 0 Solving 3.8v + -2w = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2w' to each side of the equation. 3.8v + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 3.8v + 0 = 0 + 2w 3.8v = 0 + 2w Remove the zero: 3.8v = 2w Divide each side by '3.8'. v = 0.5263157895w Simplifying v = 0.5263157895w
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