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Simplifying (2a + -1b + 3c) + (a + 5b + -4c) = 0 Remove parenthesis around (2a + -1b + 3c) 2a + -1b + 3c + (a + 5b + -4c) = 0 Remove parenthesis around (a + 5b + -4c) 2a + -1b + 3c + a + 5b + -4c = 0 Reorder the terms: 2a + a + -1b + 5b + 3c + -4c = 0 Combine like terms: 2a + a = 3a 3a + -1b + 5b + 3c + -4c = 0 Combine like terms: -1b + 5b = 4b 3a + 4b + 3c + -4c = 0 Combine like terms: 3c + -4c = -1c 3a + 4b + -1c = 0 Solving 3a + 4b + -1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 3a + 4b + -4b + -1c = 0 + -4b Combine like terms: 4b + -4b = 0 3a + 0 + -1c = 0 + -4b 3a + -1c = 0 + -4b Remove the zero: 3a + -1c = -4b Add 'c' to each side of the equation. 3a + -1c + c = -4b + c Combine like terms: -1c + c = 0 3a + 0 = -4b + c 3a = -4b + c Divide each side by '3'. a = -1.333333333b + 0.3333333333c Simplifying a = -1.333333333b + 0.3333333333c
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