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Simplifying a + 2b + 9 + -1(3a + -2b + -4c) = 0 a + 2b + 9 + (3a * -1 + -2b * -1 + -4c * -1) = 0 a + 2b + 9 + (-3a + 2b + 4c) = 0 Reorder the terms: 9 + a + -3a + 2b + 2b + 4c = 0 Combine like terms: a + -3a = -2a 9 + -2a + 2b + 2b + 4c = 0 Combine like terms: 2b + 2b = 4b 9 + -2a + 4b + 4c = 0 Solving 9 + -2a + 4b + 4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -2a + 4b + -9 + 4c = 0 + -9 Reorder the terms: 9 + -9 + -2a + 4b + 4c = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2a + 4b + 4c = 0 + -9 -2a + 4b + 4c = 0 + -9 Combine like terms: 0 + -9 = -9 -2a + 4b + 4c = -9 Add '-4b' to each side of the equation. -2a + 4b + -4b + 4c = -9 + -4b Combine like terms: 4b + -4b = 0 -2a + 0 + 4c = -9 + -4b -2a + 4c = -9 + -4b Add '-4c' to each side of the equation. -2a + 4c + -4c = -9 + -4b + -4c Combine like terms: 4c + -4c = 0 -2a + 0 = -9 + -4b + -4c -2a = -9 + -4b + -4c Divide each side by '-2'. a = 4.5 + 2b + 2c Simplifying a = 4.5 + 2b + 2c
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