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Simplifying -4c + 15c = -38d + -6d + 9(2d + 1) + -3 + 2 + 7(c + 3) Combine like terms: -4c + 15c = 11c 11c = -38d + -6d + 9(2d + 1) + -3 + 2 + 7(c + 3) Reorder the terms: 11c = -38d + -6d + 9(1 + 2d) + -3 + 2 + 7(c + 3) 11c = -38d + -6d + (1 * 9 + 2d * 9) + -3 + 2 + 7(c + 3) 11c = -38d + -6d + (9 + 18d) + -3 + 2 + 7(c + 3) Reorder the terms: 11c = -38d + -6d + 9 + 18d + -3 + 2 + 7(3 + c) 11c = -38d + -6d + 9 + 18d + -3 + 2 + (3 * 7 + c * 7) 11c = -38d + -6d + 9 + 18d + -3 + 2 + (21 + 7c) Reorder the terms: 11c = 9 + -3 + 2 + 21 + 7c + -38d + -6d + 18d Combine like terms: 9 + -3 = 6 11c = 6 + 2 + 21 + 7c + -38d + -6d + 18d Combine like terms: 6 + 2 = 8 11c = 8 + 21 + 7c + -38d + -6d + 18d Combine like terms: 8 + 21 = 29 11c = 29 + 7c + -38d + -6d + 18d Combine like terms: -38d + -6d = -44d 11c = 29 + 7c + -44d + 18d Combine like terms: -44d + 18d = -26d 11c = 29 + 7c + -26d Solving 11c = 29 + 7c + -26d Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7c' to each side of the equation. 11c + -7c = 29 + 7c + -7c + -26d Combine like terms: 11c + -7c = 4c 4c = 29 + 7c + -7c + -26d Combine like terms: 7c + -7c = 0 4c = 29 + 0 + -26d 4c = 29 + -26d Divide each side by '4'. c = 7.25 + -6.5d Simplifying c = 7.25 + -6.5d
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