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Simplifying 2(3 + y) + -5(3 + -1y) = 2(y + 4) + -3(5 + -2y) (3 * 2 + y * 2) + -5(3 + -1y) = 2(y + 4) + -3(5 + -2y) (6 + 2y) + -5(3 + -1y) = 2(y + 4) + -3(5 + -2y) 6 + 2y + (3 * -5 + -1y * -5) = 2(y + 4) + -3(5 + -2y) 6 + 2y + (-15 + 5y) = 2(y + 4) + -3(5 + -2y) Reorder the terms: 6 + -15 + 2y + 5y = 2(y + 4) + -3(5 + -2y) Combine like terms: 6 + -15 = -9 -9 + 2y + 5y = 2(y + 4) + -3(5 + -2y) Combine like terms: 2y + 5y = 7y -9 + 7y = 2(y + 4) + -3(5 + -2y) Reorder the terms: -9 + 7y = 2(4 + y) + -3(5 + -2y) -9 + 7y = (4 * 2 + y * 2) + -3(5 + -2y) -9 + 7y = (8 + 2y) + -3(5 + -2y) -9 + 7y = 8 + 2y + (5 * -3 + -2y * -3) -9 + 7y = 8 + 2y + (-15 + 6y) Reorder the terms: -9 + 7y = 8 + -15 + 2y + 6y Combine like terms: 8 + -15 = -7 -9 + 7y = -7 + 2y + 6y Combine like terms: 2y + 6y = 8y -9 + 7y = -7 + 8y Solving -9 + 7y = -7 + 8y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8y' to each side of the equation. -9 + 7y + -8y = -7 + 8y + -8y Combine like terms: 7y + -8y = -1y -9 + -1y = -7 + 8y + -8y Combine like terms: 8y + -8y = 0 -9 + -1y = -7 + 0 -9 + -1y = -7 Add '9' to each side of the equation. -9 + 9 + -1y = -7 + 9 Combine like terms: -9 + 9 = 0 0 + -1y = -7 + 9 -1y = -7 + 9 Combine like terms: -7 + 9 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2
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