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Simplifying 9(21d + 2) + 1 = 8(4d + 3) + 2 Reorder the terms: 9(2 + 21d) + 1 = 8(4d + 3) + 2 (2 * 9 + 21d * 9) + 1 = 8(4d + 3) + 2 (18 + 189d) + 1 = 8(4d + 3) + 2 Reorder the terms: 18 + 1 + 189d = 8(4d + 3) + 2 Combine like terms: 18 + 1 = 19 19 + 189d = 8(4d + 3) + 2 Reorder the terms: 19 + 189d = 8(3 + 4d) + 2 19 + 189d = (3 * 8 + 4d * 8) + 2 19 + 189d = (24 + 32d) + 2 Reorder the terms: 19 + 189d = 24 + 2 + 32d Combine like terms: 24 + 2 = 26 19 + 189d = 26 + 32d Solving 19 + 189d = 26 + 32d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-32d' to each side of the equation. 19 + 189d + -32d = 26 + 32d + -32d Combine like terms: 189d + -32d = 157d 19 + 157d = 26 + 32d + -32d Combine like terms: 32d + -32d = 0 19 + 157d = 26 + 0 19 + 157d = 26 Add '-19' to each side of the equation. 19 + -19 + 157d = 26 + -19 Combine like terms: 19 + -19 = 0 0 + 157d = 26 + -19 157d = 26 + -19 Combine like terms: 26 + -19 = 7 157d = 7 Divide each side by '157'. d = 0.04458598726 Simplifying d = 0.04458598726
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