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Simplifying 5y + 1 + -1[1 + 2(y + -1)] = 3[1 + -1(2y + -3)] Reorder the terms: 5y + 1 + -1[1 + 2(-1 + y)] = 3[1 + -1(2y + -3)] 5y + 1 + -1[1 + (-1 * 2 + y * 2)] = 3[1 + -1(2y + -3)] 5y + 1 + -1[1 + (-2 + 2y)] = 3[1 + -1(2y + -3)] Combine like terms: 1 + -2 = -1 5y + 1 + -1[-1 + 2y] = 3[1 + -1(2y + -3)] 5y + 1 + [-1 * -1 + 2y * -1] = 3[1 + -1(2y + -3)] 5y + 1 + [1 + -2y] = 3[1 + -1(2y + -3)] Reorder the terms: 1 + 1 + 5y + -2y = 3[1 + -1(2y + -3)] Combine like terms: 1 + 1 = 2 2 + 5y + -2y = 3[1 + -1(2y + -3)] Combine like terms: 5y + -2y = 3y 2 + 3y = 3[1 + -1(2y + -3)] Reorder the terms: 2 + 3y = 3[1 + -1(-3 + 2y)] 2 + 3y = 3[1 + (-3 * -1 + 2y * -1)] 2 + 3y = 3[1 + (3 + -2y)] Combine like terms: 1 + 3 = 4 2 + 3y = 3[4 + -2y] 2 + 3y = [4 * 3 + -2y * 3] 2 + 3y = [12 + -6y] Solving 2 + 3y = 12 + -6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6y' to each side of the equation. 2 + 3y + 6y = 12 + -6y + 6y Combine like terms: 3y + 6y = 9y 2 + 9y = 12 + -6y + 6y Combine like terms: -6y + 6y = 0 2 + 9y = 12 + 0 2 + 9y = 12 Add '-2' to each side of the equation. 2 + -2 + 9y = 12 + -2 Combine like terms: 2 + -2 = 0 0 + 9y = 12 + -2 9y = 12 + -2 Combine like terms: 12 + -2 = 10 9y = 10 Divide each side by '9'. y = 1.111111111 Simplifying y = 1.111111111
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