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Simplifying 2(5c + 1) + -1(4c + -5) = 5 + -1(5c + -2) Reorder the terms: 2(1 + 5c) + -1(4c + -5) = 5 + -1(5c + -2) (1 * 2 + 5c * 2) + -1(4c + -5) = 5 + -1(5c + -2) (2 + 10c) + -1(4c + -5) = 5 + -1(5c + -2) Reorder the terms: 2 + 10c + -1(-5 + 4c) = 5 + -1(5c + -2) 2 + 10c + (-5 * -1 + 4c * -1) = 5 + -1(5c + -2) 2 + 10c + (5 + -4c) = 5 + -1(5c + -2) Reorder the terms: 2 + 5 + 10c + -4c = 5 + -1(5c + -2) Combine like terms: 2 + 5 = 7 7 + 10c + -4c = 5 + -1(5c + -2) Combine like terms: 10c + -4c = 6c 7 + 6c = 5 + -1(5c + -2) Reorder the terms: 7 + 6c = 5 + -1(-2 + 5c) 7 + 6c = 5 + (-2 * -1 + 5c * -1) 7 + 6c = 5 + (2 + -5c) Combine like terms: 5 + 2 = 7 7 + 6c = 7 + -5c Add '-7' to each side of the equation. 7 + -7 + 6c = 7 + -7 + -5c Combine like terms: 7 + -7 = 0 0 + 6c = 7 + -7 + -5c 6c = 7 + -7 + -5c Combine like terms: 7 + -7 = 0 6c = 0 + -5c 6c = -5c Solving 6c = -5c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5c' to each side of the equation. 6c + 5c = -5c + 5c Combine like terms: 6c + 5c = 11c 11c = -5c + 5c Combine like terms: -5c + 5c = 0 11c = 0 Divide each side by '11'. c = 0 Simplifying c = 0
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