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Simplifying -2(Y + 1) + 3(3Y + -4) = 6(Y + -3) + 12 Reorder the terms: -2(1 + Y) + 3(3Y + -4) = 6(Y + -3) + 12 (1 * -2 + Y * -2) + 3(3Y + -4) = 6(Y + -3) + 12 (-2 + -2Y) + 3(3Y + -4) = 6(Y + -3) + 12 Reorder the terms: -2 + -2Y + 3(-4 + 3Y) = 6(Y + -3) + 12 -2 + -2Y + (-4 * 3 + 3Y * 3) = 6(Y + -3) + 12 -2 + -2Y + (-12 + 9Y) = 6(Y + -3) + 12 Reorder the terms: -2 + -12 + -2Y + 9Y = 6(Y + -3) + 12 Combine like terms: -2 + -12 = -14 -14 + -2Y + 9Y = 6(Y + -3) + 12 Combine like terms: -2Y + 9Y = 7Y -14 + 7Y = 6(Y + -3) + 12 Reorder the terms: -14 + 7Y = 6(-3 + Y) + 12 -14 + 7Y = (-3 * 6 + Y * 6) + 12 -14 + 7Y = (-18 + 6Y) + 12 Reorder the terms: -14 + 7Y = -18 + 12 + 6Y Combine like terms: -18 + 12 = -6 -14 + 7Y = -6 + 6Y Solving -14 + 7Y = -6 + 6Y Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-6Y' to each side of the equation. -14 + 7Y + -6Y = -6 + 6Y + -6Y Combine like terms: 7Y + -6Y = 1Y -14 + 1Y = -6 + 6Y + -6Y Combine like terms: 6Y + -6Y = 0 -14 + 1Y = -6 + 0 -14 + 1Y = -6 Add '14' to each side of the equation. -14 + 14 + 1Y = -6 + 14 Combine like terms: -14 + 14 = 0 0 + 1Y = -6 + 14 1Y = -6 + 14 Combine like terms: -6 + 14 = 8 1Y = 8 Divide each side by '1'. Y = 8 Simplifying Y = 8
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