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Simplifying -11(5 + -4v) + -3(7v + -10) = v + 12 + v + 5 (5 * -11 + -4v * -11) + -3(7v + -10) = v + 12 + v + 5 (-55 + 44v) + -3(7v + -10) = v + 12 + v + 5 Reorder the terms: -55 + 44v + -3(-10 + 7v) = v + 12 + v + 5 -55 + 44v + (-10 * -3 + 7v * -3) = v + 12 + v + 5 -55 + 44v + (30 + -21v) = v + 12 + v + 5 Reorder the terms: -55 + 30 + 44v + -21v = v + 12 + v + 5 Combine like terms: -55 + 30 = -25 -25 + 44v + -21v = v + 12 + v + 5 Combine like terms: 44v + -21v = 23v -25 + 23v = v + 12 + v + 5 Reorder the terms: -25 + 23v = 12 + 5 + v + v Combine like terms: 12 + 5 = 17 -25 + 23v = 17 + v + v Combine like terms: v + v = 2v -25 + 23v = 17 + 2v Solving -25 + 23v = 17 + 2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2v' to each side of the equation. -25 + 23v + -2v = 17 + 2v + -2v Combine like terms: 23v + -2v = 21v -25 + 21v = 17 + 2v + -2v Combine like terms: 2v + -2v = 0 -25 + 21v = 17 + 0 -25 + 21v = 17 Add '25' to each side of the equation. -25 + 25 + 21v = 17 + 25 Combine like terms: -25 + 25 = 0 0 + 21v = 17 + 25 21v = 17 + 25 Combine like terms: 17 + 25 = 42 21v = 42 Divide each side by '21'. v = 2 Simplifying v = 2
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