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Simplifying 42 + -1[4 + 6y + -3(y + 5)] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] Reorder the terms: 42 + -1[4 + 6y + -3(5 + y)] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] 42 + -1[4 + 6y + (5 * -3 + y * -3)] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] 42 + -1[4 + 6y + (-15 + -3y)] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] Reorder the terms: 42 + -1[4 + -15 + 6y + -3y] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] Combine like terms: 4 + -15 = -11 42 + -1[-11 + 6y + -3y] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] Combine like terms: 6y + -3y = 3y 42 + -1[-11 + 3y] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] 42 + [-11 * -1 + 3y * -1] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] 42 + [11 + -3y] = -1(4y + -5) + -1[9(y + -1) + -21y + 16] Combine like terms: 42 + 11 = 53 53 + -3y = -1(4y + -5) + -1[9(y + -1) + -21y + 16] Reorder the terms: 53 + -3y = -1(-5 + 4y) + -1[9(y + -1) + -21y + 16] 53 + -3y = (-5 * -1 + 4y * -1) + -1[9(y + -1) + -21y + 16] 53 + -3y = (5 + -4y) + -1[9(y + -1) + -21y + 16] Reorder the terms: 53 + -3y = 5 + -4y + -1[9(-1 + y) + -21y + 16] 53 + -3y = 5 + -4y + -1[(-1 * 9 + y * 9) + -21y + 16] 53 + -3y = 5 + -4y + -1[(-9 + 9y) + -21y + 16] Reorder the terms: 53 + -3y = 5 + -4y + -1[-9 + 16 + 9y + -21y] Combine like terms: -9 + 16 = 7 53 + -3y = 5 + -4y + -1[7 + 9y + -21y] Combine like terms: 9y + -21y = -12y 53 + -3y = 5 + -4y + -1[7 + -12y] 53 + -3y = 5 + -4y + [7 * -1 + -12y * -1] 53 + -3y = 5 + -4y + [-7 + 12y] Reorder the terms: 53 + -3y = 5 + -7 + -4y + 12y Combine like terms: 5 + -7 = -2 53 + -3y = -2 + -4y + 12y Combine like terms: -4y + 12y = 8y 53 + -3y = -2 + 8y Solving 53 + -3y = -2 + 8y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8y' to each side of the equation. 53 + -3y + -8y = -2 + 8y + -8y Combine like terms: -3y + -8y = -11y 53 + -11y = -2 + 8y + -8y Combine like terms: 8y + -8y = 0 53 + -11y = -2 + 0 53 + -11y = -2 Add '-53' to each side of the equation. 53 + -53 + -11y = -2 + -53 Combine like terms: 53 + -53 = 0 0 + -11y = -2 + -53 -11y = -2 + -53 Combine like terms: -2 + -53 = -55 -11y = -55 Divide each side by '-11'. y = 5 Simplifying y = 5
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