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Simplifying 48 + -1[1 + 4y + -2(y + 5)] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] Reorder the terms: 48 + -1[1 + 4y + -2(5 + y)] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] 48 + -1[1 + 4y + (5 * -2 + y * -2)] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] 48 + -1[1 + 4y + (-10 + -2y)] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] Reorder the terms: 48 + -1[1 + -10 + 4y + -2y] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] Combine like terms: 1 + -10 = -9 48 + -1[-9 + 4y + -2y] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] Combine like terms: 4y + -2y = 2y 48 + -1[-9 + 2y] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] 48 + [-9 * -1 + 2y * -1] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] 48 + [9 + -2y] = -3(3y + -7) + -1[8(y + -1) + -7y + 12] Combine like terms: 48 + 9 = 57 57 + -2y = -3(3y + -7) + -1[8(y + -1) + -7y + 12] Reorder the terms: 57 + -2y = -3(-7 + 3y) + -1[8(y + -1) + -7y + 12] 57 + -2y = (-7 * -3 + 3y * -3) + -1[8(y + -1) + -7y + 12] 57 + -2y = (21 + -9y) + -1[8(y + -1) + -7y + 12] Reorder the terms: 57 + -2y = 21 + -9y + -1[8(-1 + y) + -7y + 12] 57 + -2y = 21 + -9y + -1[(-1 * 8 + y * 8) + -7y + 12] 57 + -2y = 21 + -9y + -1[(-8 + 8y) + -7y + 12] Reorder the terms: 57 + -2y = 21 + -9y + -1[-8 + 12 + 8y + -7y] Combine like terms: -8 + 12 = 4 57 + -2y = 21 + -9y + -1[4 + 8y + -7y] Combine like terms: 8y + -7y = 1y 57 + -2y = 21 + -9y + -1[4 + 1y] 57 + -2y = 21 + -9y + [4 * -1 + 1y * -1] 57 + -2y = 21 + -9y + [-4 + -1y] Reorder the terms: 57 + -2y = 21 + -4 + -9y + -1y Combine like terms: 21 + -4 = 17 57 + -2y = 17 + -9y + -1y Combine like terms: -9y + -1y = -10y 57 + -2y = 17 + -10y Solving 57 + -2y = 17 + -10y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10y' to each side of the equation. 57 + -2y + 10y = 17 + -10y + 10y Combine like terms: -2y + 10y = 8y 57 + 8y = 17 + -10y + 10y Combine like terms: -10y + 10y = 0 57 + 8y = 17 + 0 57 + 8y = 17 Add '-57' to each side of the equation. 57 + -57 + 8y = 17 + -57 Combine like terms: 57 + -57 = 0 0 + 8y = 17 + -57 8y = 17 + -57 Combine like terms: 17 + -57 = -40 8y = -40 Divide each side by '8'. y = -5 Simplifying y = -5
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