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Simplifying 5a + 3b + 2c + -1b + 2a + -3c = 0 Reorder the terms: 5a + 2a + 3b + -1b + 2c + -3c = 0 Combine like terms: 5a + 2a = 7a 7a + 3b + -1b + 2c + -3c = 0 Combine like terms: 3b + -1b = 2b 7a + 2b + 2c + -3c = 0 Combine like terms: 2c + -3c = -1c 7a + 2b + -1c = 0 Solving 7a + 2b + -1c = 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. 7a + 2b + -2b + -1c = 0 + -2b Combine like terms: 2b + -2b = 0 7a + 0 + -1c = 0 + -2b 7a + -1c = 0 + -2b Remove the zero: 7a + -1c = -2b Add 'c' to each side of the equation. 7a + -1c + c = -2b + c Combine like terms: -1c + c = 0 7a + 0 = -2b + c 7a = -2b + c Divide each side by '7'. a = -0.2857142857b + 0.1428571429c Simplifying a = -0.2857142857b + 0.1428571429c
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