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Simplifying (a + 2b) + (3b + -4c) + (5a + -7c) + 3b = 0 Remove parenthesis around (a + 2b) a + 2b + (3b + -4c) + (5a + -7c) + 3b = 0 Remove parenthesis around (3b + -4c) a + 2b + 3b + -4c + (5a + -7c) + 3b = 0 Remove parenthesis around (5a + -7c) a + 2b + 3b + -4c + 5a + -7c + 3b = 0 Reorder the terms: a + 5a + 2b + 3b + 3b + -4c + -7c = 0 Combine like terms: a + 5a = 6a 6a + 2b + 3b + 3b + -4c + -7c = 0 Combine like terms: 2b + 3b = 5b 6a + 5b + 3b + -4c + -7c = 0 Combine like terms: 5b + 3b = 8b 6a + 8b + -4c + -7c = 0 Combine like terms: -4c + -7c = -11c 6a + 8b + -11c = 0 Solving 6a + 8b + -11c = 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. 6a + 8b + -8b + -11c = 0 + -8b Combine like terms: 8b + -8b = 0 6a + 0 + -11c = 0 + -8b 6a + -11c = 0 + -8b Remove the zero: 6a + -11c = -8b Add '11c' to each side of the equation. 6a + -11c + 11c = -8b + 11c Combine like terms: -11c + 11c = 0 6a + 0 = -8b + 11c 6a = -8b + 11c Divide each side by '6'. a = -1.333333333b + 1.833333333c Simplifying a = -1.333333333b + 1.833333333c
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