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Simplifying 19 + -1[5 + 10y + -4(y + 3)] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] Reorder the terms: 19 + -1[5 + 10y + -4(3 + y)] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] 19 + -1[5 + 10y + (3 * -4 + y * -4)] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] 19 + -1[5 + 10y + (-12 + -4y)] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] Reorder the terms: 19 + -1[5 + -12 + 10y + -4y] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] Combine like terms: 5 + -12 = -7 19 + -1[-7 + 10y + -4y] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] Combine like terms: 10y + -4y = 6y 19 + -1[-7 + 6y] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] 19 + [-7 * -1 + 6y * -1] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] 19 + [7 + -6y] = -4(3y + -7) + -1[9(y + -1) + -8y + 25] Combine like terms: 19 + 7 = 26 26 + -6y = -4(3y + -7) + -1[9(y + -1) + -8y + 25] Reorder the terms: 26 + -6y = -4(-7 + 3y) + -1[9(y + -1) + -8y + 25] 26 + -6y = (-7 * -4 + 3y * -4) + -1[9(y + -1) + -8y + 25] 26 + -6y = (28 + -12y) + -1[9(y + -1) + -8y + 25] Reorder the terms: 26 + -6y = 28 + -12y + -1[9(-1 + y) + -8y + 25] 26 + -6y = 28 + -12y + -1[(-1 * 9 + y * 9) + -8y + 25] 26 + -6y = 28 + -12y + -1[(-9 + 9y) + -8y + 25] Reorder the terms: 26 + -6y = 28 + -12y + -1[-9 + 25 + 9y + -8y] Combine like terms: -9 + 25 = 16 26 + -6y = 28 + -12y + -1[16 + 9y + -8y] Combine like terms: 9y + -8y = 1y 26 + -6y = 28 + -12y + -1[16 + 1y] 26 + -6y = 28 + -12y + [16 * -1 + 1y * -1] 26 + -6y = 28 + -12y + [-16 + -1y] Reorder the terms: 26 + -6y = 28 + -16 + -12y + -1y Combine like terms: 28 + -16 = 12 26 + -6y = 12 + -12y + -1y Combine like terms: -12y + -1y = -13y 26 + -6y = 12 + -13y Solving 26 + -6y = 12 + -13y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13y' to each side of the equation. 26 + -6y + 13y = 12 + -13y + 13y Combine like terms: -6y + 13y = 7y 26 + 7y = 12 + -13y + 13y Combine like terms: -13y + 13y = 0 26 + 7y = 12 + 0 26 + 7y = 12 Add '-26' to each side of the equation. 26 + -26 + 7y = 12 + -26 Combine like terms: 26 + -26 = 0 0 + 7y = 12 + -26 7y = 12 + -26 Combine like terms: 12 + -26 = -14 7y = -14 Divide each side by '7'. y = -2 Simplifying y = -2
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