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Simplifying 19 + -1[2 + 6y + -3(y + 4)] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] Reorder the terms: 19 + -1[2 + 6y + -3(4 + y)] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] 19 + -1[2 + 6y + (4 * -3 + y * -3)] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] 19 + -1[2 + 6y + (-12 + -3y)] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] Reorder the terms: 19 + -1[2 + -12 + 6y + -3y] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] Combine like terms: 2 + -12 = -10 19 + -1[-10 + 6y + -3y] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] Combine like terms: 6y + -3y = 3y 19 + -1[-10 + 3y] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] 19 + [-10 * -1 + 3y * -1] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] 19 + [10 + -3y] = -4(2y + -5) + -1[7(y + -1) + -9y + 16] Combine like terms: 19 + 10 = 29 29 + -3y = -4(2y + -5) + -1[7(y + -1) + -9y + 16] Reorder the terms: 29 + -3y = -4(-5 + 2y) + -1[7(y + -1) + -9y + 16] 29 + -3y = (-5 * -4 + 2y * -4) + -1[7(y + -1) + -9y + 16] 29 + -3y = (20 + -8y) + -1[7(y + -1) + -9y + 16] Reorder the terms: 29 + -3y = 20 + -8y + -1[7(-1 + y) + -9y + 16] 29 + -3y = 20 + -8y + -1[(-1 * 7 + y * 7) + -9y + 16] 29 + -3y = 20 + -8y + -1[(-7 + 7y) + -9y + 16] Reorder the terms: 29 + -3y = 20 + -8y + -1[-7 + 16 + 7y + -9y] Combine like terms: -7 + 16 = 9 29 + -3y = 20 + -8y + -1[9 + 7y + -9y] Combine like terms: 7y + -9y = -2y 29 + -3y = 20 + -8y + -1[9 + -2y] 29 + -3y = 20 + -8y + [9 * -1 + -2y * -1] 29 + -3y = 20 + -8y + [-9 + 2y] Reorder the terms: 29 + -3y = 20 + -9 + -8y + 2y Combine like terms: 20 + -9 = 11 29 + -3y = 11 + -8y + 2y Combine like terms: -8y + 2y = -6y 29 + -3y = 11 + -6y Solving 29 + -3y = 11 + -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. 29 + -3y + 6y = 11 + -6y + 6y Combine like terms: -3y + 6y = 3y 29 + 3y = 11 + -6y + 6y Combine like terms: -6y + 6y = 0 29 + 3y = 11 + 0 29 + 3y = 11 Add '-29' to each side of the equation. 29 + -29 + 3y = 11 + -29 Combine like terms: 29 + -29 = 0 0 + 3y = 11 + -29 3y = 11 + -29 Combine like terms: 11 + -29 = -18 3y = -18 Divide each side by '3'. y = -6 Simplifying y = -6
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