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Simplifying 38 + -1[5 + 6y + -3(y + 3)] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] Reorder the terms: 38 + -1[5 + 6y + -3(3 + y)] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] 38 + -1[5 + 6y + (3 * -3 + y * -3)] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] 38 + -1[5 + 6y + (-9 + -3y)] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] Reorder the terms: 38 + -1[5 + -9 + 6y + -3y] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] Combine like terms: 5 + -9 = -4 38 + -1[-4 + 6y + -3y] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] Combine like terms: 6y + -3y = 3y 38 + -1[-4 + 3y] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] 38 + [-4 * -1 + 3y * -1] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] 38 + [4 + -3y] = -3(5y + -4) + -1[7(y + -1) + -10y + 4] Combine like terms: 38 + 4 = 42 42 + -3y = -3(5y + -4) + -1[7(y + -1) + -10y + 4] Reorder the terms: 42 + -3y = -3(-4 + 5y) + -1[7(y + -1) + -10y + 4] 42 + -3y = (-4 * -3 + 5y * -3) + -1[7(y + -1) + -10y + 4] 42 + -3y = (12 + -15y) + -1[7(y + -1) + -10y + 4] Reorder the terms: 42 + -3y = 12 + -15y + -1[7(-1 + y) + -10y + 4] 42 + -3y = 12 + -15y + -1[(-1 * 7 + y * 7) + -10y + 4] 42 + -3y = 12 + -15y + -1[(-7 + 7y) + -10y + 4] Reorder the terms: 42 + -3y = 12 + -15y + -1[-7 + 4 + 7y + -10y] Combine like terms: -7 + 4 = -3 42 + -3y = 12 + -15y + -1[-3 + 7y + -10y] Combine like terms: 7y + -10y = -3y 42 + -3y = 12 + -15y + -1[-3 + -3y] 42 + -3y = 12 + -15y + [-3 * -1 + -3y * -1] 42 + -3y = 12 + -15y + [3 + 3y] Reorder the terms: 42 + -3y = 12 + 3 + -15y + 3y Combine like terms: 12 + 3 = 15 42 + -3y = 15 + -15y + 3y Combine like terms: -15y + 3y = -12y 42 + -3y = 15 + -12y Solving 42 + -3y = 15 + -12y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12y' to each side of the equation. 42 + -3y + 12y = 15 + -12y + 12y Combine like terms: -3y + 12y = 9y 42 + 9y = 15 + -12y + 12y Combine like terms: -12y + 12y = 0 42 + 9y = 15 + 0 42 + 9y = 15 Add '-42' to each side of the equation. 42 + -42 + 9y = 15 + -42 Combine like terms: 42 + -42 = 0 0 + 9y = 15 + -42 9y = 15 + -42 Combine like terms: 15 + -42 = -27 9y = -27 Divide each side by '9'. y = -3 Simplifying y = -3
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