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Simplifying 17 + -1[3 + 6y + -4(y + 5)] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] Reorder the terms: 17 + -1[3 + 6y + -4(5 + y)] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] 17 + -1[3 + 6y + (5 * -4 + y * -4)] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] 17 + -1[3 + 6y + (-20 + -4y)] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] Reorder the terms: 17 + -1[3 + -20 + 6y + -4y] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] Combine like terms: 3 + -20 = -17 17 + -1[-17 + 6y + -4y] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] Combine like terms: 6y + -4y = 2y 17 + -1[-17 + 2y] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] 17 + [-17 * -1 + 2y * -1] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] 17 + [17 + -2y] = -5(3y + -6) + -1[7(y + -1) + -18y + 21] Combine like terms: 17 + 17 = 34 34 + -2y = -5(3y + -6) + -1[7(y + -1) + -18y + 21] Reorder the terms: 34 + -2y = -5(-6 + 3y) + -1[7(y + -1) + -18y + 21] 34 + -2y = (-6 * -5 + 3y * -5) + -1[7(y + -1) + -18y + 21] 34 + -2y = (30 + -15y) + -1[7(y + -1) + -18y + 21] Reorder the terms: 34 + -2y = 30 + -15y + -1[7(-1 + y) + -18y + 21] 34 + -2y = 30 + -15y + -1[(-1 * 7 + y * 7) + -18y + 21] 34 + -2y = 30 + -15y + -1[(-7 + 7y) + -18y + 21] Reorder the terms: 34 + -2y = 30 + -15y + -1[-7 + 21 + 7y + -18y] Combine like terms: -7 + 21 = 14 34 + -2y = 30 + -15y + -1[14 + 7y + -18y] Combine like terms: 7y + -18y = -11y 34 + -2y = 30 + -15y + -1[14 + -11y] 34 + -2y = 30 + -15y + [14 * -1 + -11y * -1] 34 + -2y = 30 + -15y + [-14 + 11y] Reorder the terms: 34 + -2y = 30 + -14 + -15y + 11y Combine like terms: 30 + -14 = 16 34 + -2y = 16 + -15y + 11y Combine like terms: -15y + 11y = -4y 34 + -2y = 16 + -4y Solving 34 + -2y = 16 + -4y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4y' to each side of the equation. 34 + -2y + 4y = 16 + -4y + 4y Combine like terms: -2y + 4y = 2y 34 + 2y = 16 + -4y + 4y Combine like terms: -4y + 4y = 0 34 + 2y = 16 + 0 34 + 2y = 16 Add '-34' to each side of the equation. 34 + -34 + 2y = 16 + -34 Combine like terms: 34 + -34 = 0 0 + 2y = 16 + -34 2y = 16 + -34 Combine like terms: 16 + -34 = -18 2y = -18 Divide each side by '2'. y = -9 Simplifying y = -9
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