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Simplifying -31[1 + -1(y + 7)] + 5 = 2(4 + -1y) Reorder the terms: -31[1 + -1(7 + y)] + 5 = 2(4 + -1y) -31[1 + (7 * -1 + y * -1)] + 5 = 2(4 + -1y) -31[1 + (-7 + -1y)] + 5 = 2(4 + -1y) Combine like terms: 1 + -7 = -6 -31[-6 + -1y] + 5 = 2(4 + -1y) [-6 * -31 + -1y * -31] + 5 = 2(4 + -1y) [186 + 31y] + 5 = 2(4 + -1y) Reorder the terms: 186 + 5 + 31y = 2(4 + -1y) Combine like terms: 186 + 5 = 191 191 + 31y = 2(4 + -1y) 191 + 31y = (4 * 2 + -1y * 2) 191 + 31y = (8 + -2y) Solving 191 + 31y = 8 + -2y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2y' to each side of the equation. 191 + 31y + 2y = 8 + -2y + 2y Combine like terms: 31y + 2y = 33y 191 + 33y = 8 + -2y + 2y Combine like terms: -2y + 2y = 0 191 + 33y = 8 + 0 191 + 33y = 8 Add '-191' to each side of the equation. 191 + -191 + 33y = 8 + -191 Combine like terms: 191 + -191 = 0 0 + 33y = 8 + -191 33y = 8 + -191 Combine like terms: 8 + -191 = -183 33y = -183 Divide each side by '33'. y = -5.545454545 Simplifying y = -5.545454545
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