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Simplifying 49 + -1[1 + 8y + -2(y + 3)] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] Reorder the terms: 49 + -1[1 + 8y + -2(3 + y)] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] 49 + -1[1 + 8y + (3 * -2 + y * -2)] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] 49 + -1[1 + 8y + (-6 + -2y)] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] Reorder the terms: 49 + -1[1 + -6 + 8y + -2y] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] Combine like terms: 1 + -6 = -5 49 + -1[-5 + 8y + -2y] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] Combine like terms: 8y + -2y = 6y 49 + -1[-5 + 6y] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] 49 + [-5 * -1 + 6y * -1] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] 49 + [5 + -6y] = -4(3y + -7) + -1[9(y + -1) + -6y + 19] Combine like terms: 49 + 5 = 54 54 + -6y = -4(3y + -7) + -1[9(y + -1) + -6y + 19] Reorder the terms: 54 + -6y = -4(-7 + 3y) + -1[9(y + -1) + -6y + 19] 54 + -6y = (-7 * -4 + 3y * -4) + -1[9(y + -1) + -6y + 19] 54 + -6y = (28 + -12y) + -1[9(y + -1) + -6y + 19] Reorder the terms: 54 + -6y = 28 + -12y + -1[9(-1 + y) + -6y + 19] 54 + -6y = 28 + -12y + -1[(-1 * 9 + y * 9) + -6y + 19] 54 + -6y = 28 + -12y + -1[(-9 + 9y) + -6y + 19] Reorder the terms: 54 + -6y = 28 + -12y + -1[-9 + 19 + 9y + -6y] Combine like terms: -9 + 19 = 10 54 + -6y = 28 + -12y + -1[10 + 9y + -6y] Combine like terms: 9y + -6y = 3y 54 + -6y = 28 + -12y + -1[10 + 3y] 54 + -6y = 28 + -12y + [10 * -1 + 3y * -1] 54 + -6y = 28 + -12y + [-10 + -3y] Reorder the terms: 54 + -6y = 28 + -10 + -12y + -3y Combine like terms: 28 + -10 = 18 54 + -6y = 18 + -12y + -3y Combine like terms: -12y + -3y = -15y 54 + -6y = 18 + -15y Solving 54 + -6y = 18 + -15y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '15y' to each side of the equation. 54 + -6y + 15y = 18 + -15y + 15y Combine like terms: -6y + 15y = 9y 54 + 9y = 18 + -15y + 15y Combine like terms: -15y + 15y = 0 54 + 9y = 18 + 0 54 + 9y = 18 Add '-54' to each side of the equation. 54 + -54 + 9y = 18 + -54 Combine like terms: 54 + -54 = 0 0 + 9y = 18 + -54 9y = 18 + -54 Combine like terms: 18 + -54 = -36 9y = -36 Divide each side by '9'. y = -4 Simplifying y = -4
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