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Simplifying 500 = 45c + 35(12 + -1c) 500 = 45c + (12 * 35 + -1c * 35) 500 = 45c + (420 + -35c) Reorder the terms: 500 = 420 + 45c + -35c Combine like terms: 45c + -35c = 10c 500 = 420 + 10c Solving 500 = 420 + 10c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10c' to each side of the equation. 500 + -10c = 420 + 10c + -10c Combine like terms: 10c + -10c = 0 500 + -10c = 420 + 0 500 + -10c = 420 Add '-500' to each side of the equation. 500 + -500 + -10c = 420 + -500 Combine like terms: 500 + -500 = 0 0 + -10c = 420 + -500 -10c = 420 + -500 Combine like terms: 420 + -500 = -80 -10c = -80 Divide each side by '-10'. c = 8 Simplifying c = 8
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