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Simplifying 4(c + 1) + 2c = 7 + 3(c + 1) Reorder the terms: 4(1 + c) + 2c = 7 + 3(c + 1) (1 * 4 + c * 4) + 2c = 7 + 3(c + 1) (4 + 4c) + 2c = 7 + 3(c + 1) Combine like terms: 4c + 2c = 6c 4 + 6c = 7 + 3(c + 1) Reorder the terms: 4 + 6c = 7 + 3(1 + c) 4 + 6c = 7 + (1 * 3 + c * 3) 4 + 6c = 7 + (3 + 3c) Combine like terms: 7 + 3 = 10 4 + 6c = 10 + 3c Solving 4 + 6c = 10 + 3c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3c' to each side of the equation. 4 + 6c + -3c = 10 + 3c + -3c Combine like terms: 6c + -3c = 3c 4 + 3c = 10 + 3c + -3c Combine like terms: 3c + -3c = 0 4 + 3c = 10 + 0 4 + 3c = 10 Add '-4' to each side of the equation. 4 + -4 + 3c = 10 + -4 Combine like terms: 4 + -4 = 0 0 + 3c = 10 + -4 3c = 10 + -4 Combine like terms: 10 + -4 = 6 3c = 6 Divide each side by '3'. c = 2 Simplifying c = 2
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