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Simplifying 54 + -1[5 + 4y + -2(y + 4)] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] Reorder the terms: 54 + -1[5 + 4y + -2(4 + y)] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] 54 + -1[5 + 4y + (4 * -2 + y * -2)] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] 54 + -1[5 + 4y + (-8 + -2y)] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] Reorder the terms: 54 + -1[5 + -8 + 4y + -2y] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] Combine like terms: 5 + -8 = -3 54 + -1[-3 + 4y + -2y] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] Combine like terms: 4y + -2y = 2y 54 + -1[-3 + 2y] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] 54 + [-3 * -1 + 2y * -1] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] 54 + [3 + -2y] = -2(2y + -3) + -1[8(y + -1) + -5y + 2] Combine like terms: 54 + 3 = 57 57 + -2y = -2(2y + -3) + -1[8(y + -1) + -5y + 2] Reorder the terms: 57 + -2y = -2(-3 + 2y) + -1[8(y + -1) + -5y + 2] 57 + -2y = (-3 * -2 + 2y * -2) + -1[8(y + -1) + -5y + 2] 57 + -2y = (6 + -4y) + -1[8(y + -1) + -5y + 2] Reorder the terms: 57 + -2y = 6 + -4y + -1[8(-1 + y) + -5y + 2] 57 + -2y = 6 + -4y + -1[(-1 * 8 + y * 8) + -5y + 2] 57 + -2y = 6 + -4y + -1[(-8 + 8y) + -5y + 2] Reorder the terms: 57 + -2y = 6 + -4y + -1[-8 + 2 + 8y + -5y] Combine like terms: -8 + 2 = -6 57 + -2y = 6 + -4y + -1[-6 + 8y + -5y] Combine like terms: 8y + -5y = 3y 57 + -2y = 6 + -4y + -1[-6 + 3y] 57 + -2y = 6 + -4y + [-6 * -1 + 3y * -1] 57 + -2y = 6 + -4y + [6 + -3y] Reorder the terms: 57 + -2y = 6 + 6 + -4y + -3y Combine like terms: 6 + 6 = 12 57 + -2y = 12 + -4y + -3y Combine like terms: -4y + -3y = -7y 57 + -2y = 12 + -7y Solving 57 + -2y = 12 + -7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7y' to each side of the equation. 57 + -2y + 7y = 12 + -7y + 7y Combine like terms: -2y + 7y = 5y 57 + 5y = 12 + -7y + 7y Combine like terms: -7y + 7y = 0 57 + 5y = 12 + 0 57 + 5y = 12 Add '-57' to each side of the equation. 57 + -57 + 5y = 12 + -57 Combine like terms: 57 + -57 = 0 0 + 5y = 12 + -57 5y = 12 + -57 Combine like terms: 12 + -57 = -45 5y = -45 Divide each side by '5'. y = -9 Simplifying y = -9
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