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Simplifying -7 + -1[2 + 5y + -3(y + 2)] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] Reorder the terms: -7 + -1[2 + 5y + -3(2 + y)] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] -7 + -1[2 + 5y + (2 * -3 + y * -3)] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] -7 + -1[2 + 5y + (-6 + -3y)] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] Reorder the terms: -7 + -1[2 + -6 + 5y + -3y] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] Combine like terms: 2 + -6 = -4 -7 + -1[-4 + 5y + -3y] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] Combine like terms: 5y + -3y = 2y -7 + -1[-4 + 2y] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] -7 + [-4 * -1 + 2y * -1] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] -7 + [4 + -2y] = -11(2y + -5) + -1[2(y + -1) + -3y + 3] Combine like terms: -7 + 4 = -3 -3 + -2y = -11(2y + -5) + -1[2(y + -1) + -3y + 3] Reorder the terms: -3 + -2y = -11(-5 + 2y) + -1[2(y + -1) + -3y + 3] -3 + -2y = (-5 * -11 + 2y * -11) + -1[2(y + -1) + -3y + 3] -3 + -2y = (55 + -22y) + -1[2(y + -1) + -3y + 3] Reorder the terms: -3 + -2y = 55 + -22y + -1[2(-1 + y) + -3y + 3] -3 + -2y = 55 + -22y + -1[(-1 * 2 + y * 2) + -3y + 3] -3 + -2y = 55 + -22y + -1[(-2 + 2y) + -3y + 3] Reorder the terms: -3 + -2y = 55 + -22y + -1[-2 + 3 + 2y + -3y] Combine like terms: -2 + 3 = 1 -3 + -2y = 55 + -22y + -1[1 + 2y + -3y] Combine like terms: 2y + -3y = -1y -3 + -2y = 55 + -22y + -1[1 + -1y] -3 + -2y = 55 + -22y + [1 * -1 + -1y * -1] -3 + -2y = 55 + -22y + [-1 + 1y] Reorder the terms: -3 + -2y = 55 + -1 + -22y + 1y Combine like terms: 55 + -1 = 54 -3 + -2y = 54 + -22y + 1y Combine like terms: -22y + 1y = -21y -3 + -2y = 54 + -21y Solving -3 + -2y = 54 + -21y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '21y' to each side of the equation. -3 + -2y + 21y = 54 + -21y + 21y Combine like terms: -2y + 21y = 19y -3 + 19y = 54 + -21y + 21y Combine like terms: -21y + 21y = 0 -3 + 19y = 54 + 0 -3 + 19y = 54 Add '3' to each side of the equation. -3 + 3 + 19y = 54 + 3 Combine like terms: -3 + 3 = 0 0 + 19y = 54 + 3 19y = 54 + 3 Combine like terms: 54 + 3 = 57 19y = 57 Divide each side by '19'. y = 3 Simplifying y = 3
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