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Simplifying 24 + -1[5 + 7y + -4(y + 4)] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] Reorder the terms: 24 + -1[5 + 7y + -4(4 + y)] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] 24 + -1[5 + 7y + (4 * -4 + y * -4)] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] 24 + -1[5 + 7y + (-16 + -4y)] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] Reorder the terms: 24 + -1[5 + -16 + 7y + -4y] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] Combine like terms: 5 + -16 = -11 24 + -1[-11 + 7y + -4y] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] Combine like terms: 7y + -4y = 3y 24 + -1[-11 + 3y] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] 24 + [-11 * -1 + 3y * -1] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] 24 + [11 + -3y] = -5(5y + -3) + -1[5(y + -1) + -19y + 9] Combine like terms: 24 + 11 = 35 35 + -3y = -5(5y + -3) + -1[5(y + -1) + -19y + 9] Reorder the terms: 35 + -3y = -5(-3 + 5y) + -1[5(y + -1) + -19y + 9] 35 + -3y = (-3 * -5 + 5y * -5) + -1[5(y + -1) + -19y + 9] 35 + -3y = (15 + -25y) + -1[5(y + -1) + -19y + 9] Reorder the terms: 35 + -3y = 15 + -25y + -1[5(-1 + y) + -19y + 9] 35 + -3y = 15 + -25y + -1[(-1 * 5 + y * 5) + -19y + 9] 35 + -3y = 15 + -25y + -1[(-5 + 5y) + -19y + 9] Reorder the terms: 35 + -3y = 15 + -25y + -1[-5 + 9 + 5y + -19y] Combine like terms: -5 + 9 = 4 35 + -3y = 15 + -25y + -1[4 + 5y + -19y] Combine like terms: 5y + -19y = -14y 35 + -3y = 15 + -25y + -1[4 + -14y] 35 + -3y = 15 + -25y + [4 * -1 + -14y * -1] 35 + -3y = 15 + -25y + [-4 + 14y] Reorder the terms: 35 + -3y = 15 + -4 + -25y + 14y Combine like terms: 15 + -4 = 11 35 + -3y = 11 + -25y + 14y Combine like terms: -25y + 14y = -11y 35 + -3y = 11 + -11y Solving 35 + -3y = 11 + -11y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11y' to each side of the equation. 35 + -3y + 11y = 11 + -11y + 11y Combine like terms: -3y + 11y = 8y 35 + 8y = 11 + -11y + 11y Combine like terms: -11y + 11y = 0 35 + 8y = 11 + 0 35 + 8y = 11 Add '-35' to each side of the equation. 35 + -35 + 8y = 11 + -35 Combine like terms: 35 + -35 = 0 0 + 8y = 11 + -35 8y = 11 + -35 Combine like terms: 11 + -35 = -24 8y = -24 Divide each side by '8'. y = -3 Simplifying y = -3
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