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Simplifying 7c + 2 + -4(2c + 1) = 2c + 10 + 3(c + -3) Reorder the terms: 7c + 2 + -4(1 + 2c) = 2c + 10 + 3(c + -3) 7c + 2 + (1 * -4 + 2c * -4) = 2c + 10 + 3(c + -3) 7c + 2 + (-4 + -8c) = 2c + 10 + 3(c + -3) Reorder the terms: 2 + -4 + 7c + -8c = 2c + 10 + 3(c + -3) Combine like terms: 2 + -4 = -2 -2 + 7c + -8c = 2c + 10 + 3(c + -3) Combine like terms: 7c + -8c = -1c -2 + -1c = 2c + 10 + 3(c + -3) Reorder the terms: -2 + -1c = 2c + 10 + 3(-3 + c) -2 + -1c = 2c + 10 + (-3 * 3 + c * 3) -2 + -1c = 2c + 10 + (-9 + 3c) Reorder the terms: -2 + -1c = 10 + -9 + 2c + 3c Combine like terms: 10 + -9 = 1 -2 + -1c = 1 + 2c + 3c Combine like terms: 2c + 3c = 5c -2 + -1c = 1 + 5c Solving -2 + -1c = 1 + 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. -2 + -1c + -5c = 1 + 5c + -5c Combine like terms: -1c + -5c = -6c -2 + -6c = 1 + 5c + -5c Combine like terms: 5c + -5c = 0 -2 + -6c = 1 + 0 -2 + -6c = 1 Add '2' to each side of the equation. -2 + 2 + -6c = 1 + 2 Combine like terms: -2 + 2 = 0 0 + -6c = 1 + 2 -6c = 1 + 2 Combine like terms: 1 + 2 = 3 -6c = 3 Divide each side by '-6'. c = -0.5 Simplifying c = -0.5
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