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Simplifying 17(5c + -1) + -12 = 83c + 17 Reorder the terms: 17(-1 + 5c) + -12 = 83c + 17 (-1 * 17 + 5c * 17) + -12 = 83c + 17 (-17 + 85c) + -12 = 83c + 17 Reorder the terms: -17 + -12 + 85c = 83c + 17 Combine like terms: -17 + -12 = -29 -29 + 85c = 83c + 17 Reorder the terms: -29 + 85c = 17 + 83c Solving -29 + 85c = 17 + 83c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-83c' to each side of the equation. -29 + 85c + -83c = 17 + 83c + -83c Combine like terms: 85c + -83c = 2c -29 + 2c = 17 + 83c + -83c Combine like terms: 83c + -83c = 0 -29 + 2c = 17 + 0 -29 + 2c = 17 Add '29' to each side of the equation. -29 + 29 + 2c = 17 + 29 Combine like terms: -29 + 29 = 0 0 + 2c = 17 + 29 2c = 17 + 29 Combine like terms: 17 + 29 = 46 2c = 46 Divide each side by '2'. c = 23 Simplifying c = 23
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