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Simplifying (3a + 5b + -4c) + (2a + -3b + -1c) = 0 Remove parenthesis around (3a + 5b + -4c) 3a + 5b + -4c + (2a + -3b + -1c) = 0 Remove parenthesis around (2a + -3b + -1c) 3a + 5b + -4c + 2a + -3b + -1c = 0 Reorder the terms: 3a + 2a + 5b + -3b + -4c + -1c = 0 Combine like terms: 3a + 2a = 5a 5a + 5b + -3b + -4c + -1c = 0 Combine like terms: 5b + -3b = 2b 5a + 2b + -4c + -1c = 0 Combine like terms: -4c + -1c = -5c 5a + 2b + -5c = 0 Solving 5a + 2b + -5c = 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. 5a + 2b + -2b + -5c = 0 + -2b Combine like terms: 2b + -2b = 0 5a + 0 + -5c = 0 + -2b 5a + -5c = 0 + -2b Remove the zero: 5a + -5c = -2b Add '5c' to each side of the equation. 5a + -5c + 5c = -2b + 5c Combine like terms: -5c + 5c = 0 5a + 0 = -2b + 5c 5a = -2b + 5c Divide each side by '5'. a = -0.4b + c Simplifying a = -0.4b + c
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