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Simplifying 12(7c + -1) + -10 = 82c + 12 Reorder the terms: 12(-1 + 7c) + -10 = 82c + 12 (-1 * 12 + 7c * 12) + -10 = 82c + 12 (-12 + 84c) + -10 = 82c + 12 Reorder the terms: -12 + -10 + 84c = 82c + 12 Combine like terms: -12 + -10 = -22 -22 + 84c = 82c + 12 Reorder the terms: -22 + 84c = 12 + 82c Solving -22 + 84c = 12 + 82c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-82c' to each side of the equation. -22 + 84c + -82c = 12 + 82c + -82c Combine like terms: 84c + -82c = 2c -22 + 2c = 12 + 82c + -82c Combine like terms: 82c + -82c = 0 -22 + 2c = 12 + 0 -22 + 2c = 12 Add '22' to each side of the equation. -22 + 22 + 2c = 12 + 22 Combine like terms: -22 + 22 = 0 0 + 2c = 12 + 22 2c = 12 + 22 Combine like terms: 12 + 22 = 34 2c = 34 Divide each side by '2'. c = 17 Simplifying c = 17
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