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Simplifying 5a + 6b + -2c + a + -4b + -1c = 0 Reorder the terms: 5a + a + 6b + -4b + -2c + -1c = 0 Combine like terms: 5a + a = 6a 6a + 6b + -4b + -2c + -1c = 0 Combine like terms: 6b + -4b = 2b 6a + 2b + -2c + -1c = 0 Combine like terms: -2c + -1c = -3c 6a + 2b + -3c = 0 Solving 6a + 2b + -3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 6a + 2b + -2b + -3c = 0 + -2b Combine like terms: 2b + -2b = 0 6a + 0 + -3c = 0 + -2b 6a + -3c = 0 + -2b Remove the zero: 6a + -3c = -2b Add '3c' to each side of the equation. 6a + -3c + 3c = -2b + 3c Combine like terms: -3c + 3c = 0 6a + 0 = -2b + 3c 6a = -2b + 3c Divide each side by '6'. a = -0.3333333333b + 0.5c Simplifying a = -0.3333333333b + 0.5c
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