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Simplifying -6(y + 1) + 3(4y + -3) = 5(y + -3) + 8 Reorder the terms: -6(1 + y) + 3(4y + -3) = 5(y + -3) + 8 (1 * -6 + y * -6) + 3(4y + -3) = 5(y + -3) + 8 (-6 + -6y) + 3(4y + -3) = 5(y + -3) + 8 Reorder the terms: -6 + -6y + 3(-3 + 4y) = 5(y + -3) + 8 -6 + -6y + (-3 * 3 + 4y * 3) = 5(y + -3) + 8 -6 + -6y + (-9 + 12y) = 5(y + -3) + 8 Reorder the terms: -6 + -9 + -6y + 12y = 5(y + -3) + 8 Combine like terms: -6 + -9 = -15 -15 + -6y + 12y = 5(y + -3) + 8 Combine like terms: -6y + 12y = 6y -15 + 6y = 5(y + -3) + 8 Reorder the terms: -15 + 6y = 5(-3 + y) + 8 -15 + 6y = (-3 * 5 + y * 5) + 8 -15 + 6y = (-15 + 5y) + 8 Reorder the terms: -15 + 6y = -15 + 8 + 5y Combine like terms: -15 + 8 = -7 -15 + 6y = -7 + 5y Solving -15 + 6y = -7 + 5y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5y' to each side of the equation. -15 + 6y + -5y = -7 + 5y + -5y Combine like terms: 6y + -5y = 1y -15 + 1y = -7 + 5y + -5y Combine like terms: 5y + -5y = 0 -15 + 1y = -7 + 0 -15 + 1y = -7 Add '15' to each side of the equation. -15 + 15 + 1y = -7 + 15 Combine like terms: -15 + 15 = 0 0 + 1y = -7 + 15 1y = -7 + 15 Combine like terms: -7 + 15 = 8 1y = 8 Divide each side by '1'. y = 8 Simplifying y = 8
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