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Simplifying v + -2 + 7v + -2 = -3(12v + -11) + -7(8v + -9) Reorder the terms: -2 + -2 + v + 7v = -3(12v + -11) + -7(8v + -9) Combine like terms: -2 + -2 = -4 -4 + v + 7v = -3(12v + -11) + -7(8v + -9) Combine like terms: v + 7v = 8v -4 + 8v = -3(12v + -11) + -7(8v + -9) Reorder the terms: -4 + 8v = -3(-11 + 12v) + -7(8v + -9) -4 + 8v = (-11 * -3 + 12v * -3) + -7(8v + -9) -4 + 8v = (33 + -36v) + -7(8v + -9) Reorder the terms: -4 + 8v = 33 + -36v + -7(-9 + 8v) -4 + 8v = 33 + -36v + (-9 * -7 + 8v * -7) -4 + 8v = 33 + -36v + (63 + -56v) Reorder the terms: -4 + 8v = 33 + 63 + -36v + -56v Combine like terms: 33 + 63 = 96 -4 + 8v = 96 + -36v + -56v Combine like terms: -36v + -56v = -92v -4 + 8v = 96 + -92v Solving -4 + 8v = 96 + -92v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '92v' to each side of the equation. -4 + 8v + 92v = 96 + -92v + 92v Combine like terms: 8v + 92v = 100v -4 + 100v = 96 + -92v + 92v Combine like terms: -92v + 92v = 0 -4 + 100v = 96 + 0 -4 + 100v = 96 Add '4' to each side of the equation. -4 + 4 + 100v = 96 + 4 Combine like terms: -4 + 4 = 0 0 + 100v = 96 + 4 100v = 96 + 4 Combine like terms: 96 + 4 = 100 100v = 100 Divide each side by '100'. v = 1 Simplifying v = 1
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