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Simplifying 5x + -3x + x + 8 = 2x + 1 + x + c Reorder the terms: 8 + 5x + -3x + x = 2x + 1 + x + c Combine like terms: 5x + -3x = 2x 8 + 2x + x = 2x + 1 + x + c Combine like terms: 2x + x = 3x 8 + 3x = 2x + 1 + x + c Reorder the terms: 8 + 3x = 1 + c + 2x + x Combine like terms: 2x + x = 3x 8 + 3x = 1 + c + 3x Add '-3x' to each side of the equation. 8 + 3x + -3x = 1 + c + 3x + -3x Combine like terms: 3x + -3x = 0 8 + 0 = 1 + c + 3x + -3x 8 = 1 + c + 3x + -3x Combine like terms: 3x + -3x = 0 8 = 1 + c + 0 8 = 1 + c Solving 8 = 1 + c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1c' to each side of the equation. 8 + -1c = 1 + c + -1c Combine like terms: c + -1c = 0 8 + -1c = 1 + 0 8 + -1c = 1 Add '-8' to each side of the equation. 8 + -8 + -1c = 1 + -8 Combine like terms: 8 + -8 = 0 0 + -1c = 1 + -8 -1c = 1 + -8 Combine like terms: 1 + -8 = -7 -1c = -7 Divide each side by '-1'. c = 7 Simplifying c = 7
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