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Simplifying 23 + -1[3 + 9y + -3(y + 3)] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] Reorder the terms: 23 + -1[3 + 9y + -3(3 + y)] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] 23 + -1[3 + 9y + (3 * -3 + y * -3)] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] 23 + -1[3 + 9y + (-9 + -3y)] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] Reorder the terms: 23 + -1[3 + -9 + 9y + -3y] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] Combine like terms: 3 + -9 = -6 23 + -1[-6 + 9y + -3y] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] Combine like terms: 9y + -3y = 6y 23 + -1[-6 + 6y] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] 23 + [-6 * -1 + 6y * -1] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] 23 + [6 + -6y] = -3(4y + -6) + -1[8(y + -1) + -10y + 13] Combine like terms: 23 + 6 = 29 29 + -6y = -3(4y + -6) + -1[8(y + -1) + -10y + 13] Reorder the terms: 29 + -6y = -3(-6 + 4y) + -1[8(y + -1) + -10y + 13] 29 + -6y = (-6 * -3 + 4y * -3) + -1[8(y + -1) + -10y + 13] 29 + -6y = (18 + -12y) + -1[8(y + -1) + -10y + 13] Reorder the terms: 29 + -6y = 18 + -12y + -1[8(-1 + y) + -10y + 13] 29 + -6y = 18 + -12y + -1[(-1 * 8 + y * 8) + -10y + 13] 29 + -6y = 18 + -12y + -1[(-8 + 8y) + -10y + 13] Reorder the terms: 29 + -6y = 18 + -12y + -1[-8 + 13 + 8y + -10y] Combine like terms: -8 + 13 = 5 29 + -6y = 18 + -12y + -1[5 + 8y + -10y] Combine like terms: 8y + -10y = -2y 29 + -6y = 18 + -12y + -1[5 + -2y] 29 + -6y = 18 + -12y + [5 * -1 + -2y * -1] 29 + -6y = 18 + -12y + [-5 + 2y] Reorder the terms: 29 + -6y = 18 + -5 + -12y + 2y Combine like terms: 18 + -5 = 13 29 + -6y = 13 + -12y + 2y Combine like terms: -12y + 2y = -10y 29 + -6y = 13 + -10y Solving 29 + -6y = 13 + -10y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10y' to each side of the equation. 29 + -6y + 10y = 13 + -10y + 10y Combine like terms: -6y + 10y = 4y 29 + 4y = 13 + -10y + 10y Combine like terms: -10y + 10y = 0 29 + 4y = 13 + 0 29 + 4y = 13 Add '-29' to each side of the equation. 29 + -29 + 4y = 13 + -29 Combine like terms: 29 + -29 = 0 0 + 4y = 13 + -29 4y = 13 + -29 Combine like terms: 13 + -29 = -16 4y = -16 Divide each side by '4'. y = -4 Simplifying y = -4
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