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Simplifying (3a + 4b + -1c) + (a + 6b + 4c) = 0 Remove parenthesis around (3a + 4b + -1c) 3a + 4b + -1c + (a + 6b + 4c) = 0 Remove parenthesis around (a + 6b + 4c) 3a + 4b + -1c + a + 6b + 4c = 0 Reorder the terms: 3a + a + 4b + 6b + -1c + 4c = 0 Combine like terms: 3a + a = 4a 4a + 4b + 6b + -1c + 4c = 0 Combine like terms: 4b + 6b = 10b 4a + 10b + -1c + 4c = 0 Combine like terms: -1c + 4c = 3c 4a + 10b + 3c = 0 Solving 4a + 10b + 3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10b' to each side of the equation. 4a + 10b + -10b + 3c = 0 + -10b Combine like terms: 10b + -10b = 0 4a + 0 + 3c = 0 + -10b 4a + 3c = 0 + -10b Remove the zero: 4a + 3c = -10b Add '-3c' to each side of the equation. 4a + 3c + -3c = -10b + -3c Combine like terms: 3c + -3c = 0 4a + 0 = -10b + -3c 4a = -10b + -3c Divide each side by '4'. a = -2.5b + -0.75c Simplifying a = -2.5b + -0.75c
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