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Simplifying 4(1 + 5v) + 7(-5 + -3v) = 0 (1 * 4 + 5v * 4) + 7(-5 + -3v) = 0 (4 + 20v) + 7(-5 + -3v) = 0 4 + 20v + (-5 * 7 + -3v * 7) = 0 4 + 20v + (-35 + -21v) = 0 Reorder the terms: 4 + -35 + 20v + -21v = 0 Combine like terms: 4 + -35 = -31 -31 + 20v + -21v = 0 Combine like terms: 20v + -21v = -1v -31 + -1v = 0 Solving -31 + -1v = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + -1v = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -1v = 0 + 31 -1v = 0 + 31 Combine like terms: 0 + 31 = 31 -1v = 31 Divide each side by '-1'. v = -31 Simplifying v = -31
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