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Simplifying 15 + -1[2 + 8y + -3(y + 2)] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] Reorder the terms: 15 + -1[2 + 8y + -3(2 + y)] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] 15 + -1[2 + 8y + (2 * -3 + y * -3)] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] 15 + -1[2 + 8y + (-6 + -3y)] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] Reorder the terms: 15 + -1[2 + -6 + 8y + -3y] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] Combine like terms: 2 + -6 = -4 15 + -1[-4 + 8y + -3y] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] Combine like terms: 8y + -3y = 5y 15 + -1[-4 + 5y] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] 15 + [-4 * -1 + 5y * -1] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] 15 + [4 + -5y] = -4(2y + -3) + -1[7(y + -1) + -8y + 6] Combine like terms: 15 + 4 = 19 19 + -5y = -4(2y + -3) + -1[7(y + -1) + -8y + 6] Reorder the terms: 19 + -5y = -4(-3 + 2y) + -1[7(y + -1) + -8y + 6] 19 + -5y = (-3 * -4 + 2y * -4) + -1[7(y + -1) + -8y + 6] 19 + -5y = (12 + -8y) + -1[7(y + -1) + -8y + 6] Reorder the terms: 19 + -5y = 12 + -8y + -1[7(-1 + y) + -8y + 6] 19 + -5y = 12 + -8y + -1[(-1 * 7 + y * 7) + -8y + 6] 19 + -5y = 12 + -8y + -1[(-7 + 7y) + -8y + 6] Reorder the terms: 19 + -5y = 12 + -8y + -1[-7 + 6 + 7y + -8y] Combine like terms: -7 + 6 = -1 19 + -5y = 12 + -8y + -1[-1 + 7y + -8y] Combine like terms: 7y + -8y = -1y 19 + -5y = 12 + -8y + -1[-1 + -1y] 19 + -5y = 12 + -8y + [-1 * -1 + -1y * -1] 19 + -5y = 12 + -8y + [1 + 1y] Reorder the terms: 19 + -5y = 12 + 1 + -8y + 1y Combine like terms: 12 + 1 = 13 19 + -5y = 13 + -8y + 1y Combine like terms: -8y + 1y = -7y 19 + -5y = 13 + -7y Solving 19 + -5y = 13 + -7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7y' to each side of the equation. 19 + -5y + 7y = 13 + -7y + 7y Combine like terms: -5y + 7y = 2y 19 + 2y = 13 + -7y + 7y Combine like terms: -7y + 7y = 0 19 + 2y = 13 + 0 19 + 2y = 13 Add '-19' to each side of the equation. 19 + -19 + 2y = 13 + -19 Combine like terms: 19 + -19 = 0 0 + 2y = 13 + -19 2y = 13 + -19 Combine like terms: 13 + -19 = -6 2y = -6 Divide each side by '2'. y = -3 Simplifying y = -3
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