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Simplifying (9a + -6b + -5c) + -1(5a + 5b + -2c) = 0 Remove parenthesis around (9a + -6b + -5c) 9a + -6b + -5c + -1(5a + 5b + -2c) = 0 9a + -6b + -5c + (5a * -1 + 5b * -1 + -2c * -1) = 0 9a + -6b + -5c + (-5a + -5b + 2c) = 0 Reorder the terms: 9a + -5a + -6b + -5b + -5c + 2c = 0 Combine like terms: 9a + -5a = 4a 4a + -6b + -5b + -5c + 2c = 0 Combine like terms: -6b + -5b = -11b 4a + -11b + -5c + 2c = 0 Combine like terms: -5c + 2c = -3c 4a + -11b + -3c = 0 Solving 4a + -11b + -3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11b' to each side of the equation. 4a + -11b + 11b + -3c = 0 + 11b Combine like terms: -11b + 11b = 0 4a + 0 + -3c = 0 + 11b 4a + -3c = 0 + 11b Remove the zero: 4a + -3c = 11b Add '3c' to each side of the equation. 4a + -3c + 3c = 11b + 3c Combine like terms: -3c + 3c = 0 4a + 0 = 11b + 3c 4a = 11b + 3c Divide each side by '4'. a = 2.75b + 0.75c Simplifying a = 2.75b + 0.75c
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