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Simplifying 5a + 6b + 7c + -3c + 2b + -1a = 0 Reorder the terms: 5a + -1a + 6b + 2b + 7c + -3c = 0 Combine like terms: 5a + -1a = 4a 4a + 6b + 2b + 7c + -3c = 0 Combine like terms: 6b + 2b = 8b 4a + 8b + 7c + -3c = 0 Combine like terms: 7c + -3c = 4c 4a + 8b + 4c = 0 Solving 4a + 8b + 4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 4a + 8b + -8b + 4c = 0 + -8b Combine like terms: 8b + -8b = 0 4a + 0 + 4c = 0 + -8b 4a + 4c = 0 + -8b Remove the zero: 4a + 4c = -8b Add '-4c' to each side of the equation. 4a + 4c + -4c = -8b + -4c Combine like terms: 4c + -4c = 0 4a + 0 = -8b + -4c 4a = -8b + -4c Divide each side by '4'. a = -2b + -1c Simplifying a = -2b + -1c
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