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Simplifying 2d + d + 7 + 5[40 + -1(2d + -7)] = 81 Reorder the terms: 2d + d + 7 + 5[40 + -1(-7 + 2d)] = 81 2d + d + 7 + 5[40 + (-7 * -1 + 2d * -1)] = 81 2d + d + 7 + 5[40 + (7 + -2d)] = 81 Combine like terms: 40 + 7 = 47 2d + d + 7 + 5[47 + -2d] = 81 2d + d + 7 + [47 * 5 + -2d * 5] = 81 2d + d + 7 + [235 + -10d] = 81 Reorder the terms: 7 + 235 + 2d + d + -10d = 81 Combine like terms: 7 + 235 = 242 242 + 2d + d + -10d = 81 Combine like terms: 2d + d = 3d 242 + 3d + -10d = 81 Combine like terms: 3d + -10d = -7d 242 + -7d = 81 Solving 242 + -7d = 81 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-242' to each side of the equation. 242 + -242 + -7d = 81 + -242 Combine like terms: 242 + -242 = 0 0 + -7d = 81 + -242 -7d = 81 + -242 Combine like terms: 81 + -242 = -161 -7d = -161 Divide each side by '-7'. d = 23 Simplifying d = 23
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