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Simplifying (d) + (d + 5) + (d + -10) + (2d) + (d + -10) * 0.5 = 111 d + (d + 5) + (d + -10) + (2d) + (d + -10) * 0.5 = 111 Reorder the terms: d + (5 + d) + (d + -10) + (2d) + (d + -10) * 0.5 = 111 Remove parenthesis around (5 + d) d + 5 + d + (d + -10) + (2d) + (d + -10) * 0.5 = 111 Reorder the terms: d + 5 + d + (-10 + d) + (2d) + (d + -10) * 0.5 = 111 Remove parenthesis around (-10 + d) d + 5 + d + -10 + d + (2d) + (d + -10) * 0.5 = 111 Reorder the terms: d + 5 + d + -10 + d + (2d) + (-10 + d) * 0.5 = 111 Reorder the terms for easier multiplication: d + 5 + d + -10 + d + (2d) + 0.5(-10 + d) = 111 d + 5 + d + -10 + d + (2d) + (-10 * 0.5 + d * 0.5) = 111 d + 5 + d + -10 + d + (2d) + (-5 + 0.5d) = 111 Reorder the terms: 5 + -10 + -5 + d + d + d + (2d) + 0.5d = 111 Combine like terms: 5 + -10 = -5 -5 + -5 + d + d + d + (2d) + 0.5d = 111 Combine like terms: -5 + -5 = -10 -10 + d + d + d + (2d) + 0.5d = 111 Combine like terms: d + d = 2d -10 + 2d + d + (2d) + 0.5d = 111 Combine like terms: 2d + d = 3d -10 + 3d + (2d) + 0.5d = 111 Combine like terms: 3d + (2d) = 5d -10 + 5d + 0.5d = 111 Combine like terms: 5d + 0.5d = 5.5d -10 + 5.5d = 111 Solving -10 + 5.5d = 111 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 5.5d = 111 + 10 Combine like terms: -10 + 10 = 0 0 + 5.5d = 111 + 10 5.5d = 111 + 10 Combine like terms: 111 + 10 = 121 5.5d = 121 Divide each side by '5.5'. d = 22 Simplifying d = 22
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