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Simplifying 4(1 + -7v) + -4(4 + -7v) = -1v + -2v (1 * 4 + -7v * 4) + -4(4 + -7v) = -1v + -2v (4 + -28v) + -4(4 + -7v) = -1v + -2v 4 + -28v + (4 * -4 + -7v * -4) = -1v + -2v 4 + -28v + (-16 + 28v) = -1v + -2v Reorder the terms: 4 + -16 + -28v + 28v = -1v + -2v Combine like terms: 4 + -16 = -12 -12 + -28v + 28v = -1v + -2v Combine like terms: -28v + 28v = 0 -12 + 0 = -1v + -2v -12 = -1v + -2v Combine like terms: -1v + -2v = -3v -12 = -3v Solving -12 = -3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3v' to each side of the equation. -12 + 3v = -3v + 3v Combine like terms: -3v + 3v = 0 -12 + 3v = 0 Add '12' to each side of the equation. -12 + 12 + 3v = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 3v = 0 + 12 3v = 0 + 12 Combine like terms: 0 + 12 = 12 3v = 12 Divide each side by '3'. v = 4 Simplifying v = 4
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