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Simplifying 21 + -1[2 + 9y + -4(y + 3)] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] Reorder the terms: 21 + -1[2 + 9y + -4(3 + y)] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] 21 + -1[2 + 9y + (3 * -4 + y * -4)] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] 21 + -1[2 + 9y + (-12 + -4y)] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] Reorder the terms: 21 + -1[2 + -12 + 9y + -4y] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] Combine like terms: 2 + -12 = -10 21 + -1[-10 + 9y + -4y] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] Combine like terms: 9y + -4y = 5y 21 + -1[-10 + 5y] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] 21 + [-10 * -1 + 5y * -1] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] 21 + [10 + -5y] = -4(5y + -4) + -1[9(y + -1) + -20y + 6] Combine like terms: 21 + 10 = 31 31 + -5y = -4(5y + -4) + -1[9(y + -1) + -20y + 6] Reorder the terms: 31 + -5y = -4(-4 + 5y) + -1[9(y + -1) + -20y + 6] 31 + -5y = (-4 * -4 + 5y * -4) + -1[9(y + -1) + -20y + 6] 31 + -5y = (16 + -20y) + -1[9(y + -1) + -20y + 6] Reorder the terms: 31 + -5y = 16 + -20y + -1[9(-1 + y) + -20y + 6] 31 + -5y = 16 + -20y + -1[(-1 * 9 + y * 9) + -20y + 6] 31 + -5y = 16 + -20y + -1[(-9 + 9y) + -20y + 6] Reorder the terms: 31 + -5y = 16 + -20y + -1[-9 + 6 + 9y + -20y] Combine like terms: -9 + 6 = -3 31 + -5y = 16 + -20y + -1[-3 + 9y + -20y] Combine like terms: 9y + -20y = -11y 31 + -5y = 16 + -20y + -1[-3 + -11y] 31 + -5y = 16 + -20y + [-3 * -1 + -11y * -1] 31 + -5y = 16 + -20y + [3 + 11y] Reorder the terms: 31 + -5y = 16 + 3 + -20y + 11y Combine like terms: 16 + 3 = 19 31 + -5y = 19 + -20y + 11y Combine like terms: -20y + 11y = -9y 31 + -5y = 19 + -9y Solving 31 + -5y = 19 + -9y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9y' to each side of the equation. 31 + -5y + 9y = 19 + -9y + 9y Combine like terms: -5y + 9y = 4y 31 + 4y = 19 + -9y + 9y Combine like terms: -9y + 9y = 0 31 + 4y = 19 + 0 31 + 4y = 19 Add '-31' to each side of the equation. 31 + -31 + 4y = 19 + -31 Combine like terms: 31 + -31 = 0 0 + 4y = 19 + -31 4y = 19 + -31 Combine like terms: 19 + -31 = -12 4y = -12 Divide each side by '4'. y = -3 Simplifying y = -3
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