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Simplifying 45 + -1[2 + 6y + -2(y + 3)] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] Reorder the terms: 45 + -1[2 + 6y + -2(3 + y)] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] 45 + -1[2 + 6y + (3 * -2 + y * -2)] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] 45 + -1[2 + 6y + (-6 + -2y)] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] Reorder the terms: 45 + -1[2 + -6 + 6y + -2y] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] Combine like terms: 2 + -6 = -4 45 + -1[-4 + 6y + -2y] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] Combine like terms: 6y + -2y = 4y 45 + -1[-4 + 4y] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] 45 + [-4 * -1 + 4y * -1] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] 45 + [4 + -4y] = -3(5y + -1) + -1[5(y + -1) + -7y + 13] Combine like terms: 45 + 4 = 49 49 + -4y = -3(5y + -1) + -1[5(y + -1) + -7y + 13] Reorder the terms: 49 + -4y = -3(-1 + 5y) + -1[5(y + -1) + -7y + 13] 49 + -4y = (-1 * -3 + 5y * -3) + -1[5(y + -1) + -7y + 13] 49 + -4y = (3 + -15y) + -1[5(y + -1) + -7y + 13] Reorder the terms: 49 + -4y = 3 + -15y + -1[5(-1 + y) + -7y + 13] 49 + -4y = 3 + -15y + -1[(-1 * 5 + y * 5) + -7y + 13] 49 + -4y = 3 + -15y + -1[(-5 + 5y) + -7y + 13] Reorder the terms: 49 + -4y = 3 + -15y + -1[-5 + 13 + 5y + -7y] Combine like terms: -5 + 13 = 8 49 + -4y = 3 + -15y + -1[8 + 5y + -7y] Combine like terms: 5y + -7y = -2y 49 + -4y = 3 + -15y + -1[8 + -2y] 49 + -4y = 3 + -15y + [8 * -1 + -2y * -1] 49 + -4y = 3 + -15y + [-8 + 2y] Reorder the terms: 49 + -4y = 3 + -8 + -15y + 2y Combine like terms: 3 + -8 = -5 49 + -4y = -5 + -15y + 2y Combine like terms: -15y + 2y = -13y 49 + -4y = -5 + -13y Solving 49 + -4y = -5 + -13y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13y' to each side of the equation. 49 + -4y + 13y = -5 + -13y + 13y Combine like terms: -4y + 13y = 9y 49 + 9y = -5 + -13y + 13y Combine like terms: -13y + 13y = 0 49 + 9y = -5 + 0 49 + 9y = -5 Add '-49' to each side of the equation. 49 + -49 + 9y = -5 + -49 Combine like terms: 49 + -49 = 0 0 + 9y = -5 + -49 9y = -5 + -49 Combine like terms: -5 + -49 = -54 9y = -54 Divide each side by '9'. y = -6 Simplifying y = -6
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