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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 = 33 2d + d + 7 + 5[33 + -2d] = 81 2d + d + 7 + [33 * 5 + -2d * 5] = 81 2d + d + 7 + [165 + -10d] = 81 Reorder the terms: 7 + 165 + 2d + d + -10d = 81 Combine like terms: 7 + 165 = 172 172 + 2d + d + -10d = 81 Combine like terms: 2d + d = 3d 172 + 3d + -10d = 81 Combine like terms: 3d + -10d = -7d 172 + -7d = 81 Solving 172 + -7d = 81 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-172' to each side of the equation. 172 + -172 + -7d = 81 + -172 Combine like terms: 172 + -172 = 0 0 + -7d = 81 + -172 -7d = 81 + -172 Combine like terms: 81 + -172 = -91 -7d = -91 Divide each side by '-7'. d = 13 Simplifying d = 13
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