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Simplifying 2(2y + -9) + -1(12 + -30y) = 12 + -6(-5y + 3) Reorder the terms: 2(-9 + 2y) + -1(12 + -30y) = 12 + -6(-5y + 3) (-9 * 2 + 2y * 2) + -1(12 + -30y) = 12 + -6(-5y + 3) (-18 + 4y) + -1(12 + -30y) = 12 + -6(-5y + 3) -18 + 4y + (12 * -1 + -30y * -1) = 12 + -6(-5y + 3) -18 + 4y + (-12 + 30y) = 12 + -6(-5y + 3) Reorder the terms: -18 + -12 + 4y + 30y = 12 + -6(-5y + 3) Combine like terms: -18 + -12 = -30 -30 + 4y + 30y = 12 + -6(-5y + 3) Combine like terms: 4y + 30y = 34y -30 + 34y = 12 + -6(-5y + 3) Reorder the terms: -30 + 34y = 12 + -6(3 + -5y) -30 + 34y = 12 + (3 * -6 + -5y * -6) -30 + 34y = 12 + (-18 + 30y) Combine like terms: 12 + -18 = -6 -30 + 34y = -6 + 30y Solving -30 + 34y = -6 + 30y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-30y' to each side of the equation. -30 + 34y + -30y = -6 + 30y + -30y Combine like terms: 34y + -30y = 4y -30 + 4y = -6 + 30y + -30y Combine like terms: 30y + -30y = 0 -30 + 4y = -6 + 0 -30 + 4y = -6 Add '30' to each side of the equation. -30 + 30 + 4y = -6 + 30 Combine like terms: -30 + 30 = 0 0 + 4y = -6 + 30 4y = -6 + 30 Combine like terms: -6 + 30 = 24 4y = 24 Divide each side by '4'. y = 6 Simplifying y = 6
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