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Simplifying (3a + -2b + c) + -1(a + -3b + c) = 0 Remove parenthesis around (3a + -2b + c) 3a + -2b + c + -1(a + -3b + c) = 0 3a + -2b + c + (a * -1 + -3b * -1 + c * -1) = 0 3a + -2b + c + (-1a + 3b + -1c) = 0 Reorder the terms: 3a + -1a + -2b + 3b + c + -1c = 0 Combine like terms: 3a + -1a = 2a 2a + -2b + 3b + c + -1c = 0 Combine like terms: -2b + 3b = 1b 2a + 1b + c + -1c = 0 Combine like terms: c + -1c = 0 2a + 1b + 0 = 0 2a + 1b = 0 Solving 2a + 1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 2a + 1b + -1b = 0 + -1b Combine like terms: 1b + -1b = 0 2a + 0 = 0 + -1b 2a = 0 + -1b Remove the zero: 2a = -1b Divide each side by '2'. a = -0.5b Simplifying a = -0.5b
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