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Simplifying 3(a + b) + -1(a + -2b) = 0 (a * 3 + b * 3) + -1(a + -2b) = 0 (3a + 3b) + -1(a + -2b) = 0 3a + 3b + (a * -1 + -2b * -1) = 0 3a + 3b + (-1a + 2b) = 0 Reorder the terms: 3a + -1a + 3b + 2b = 0 Combine like terms: 3a + -1a = 2a 2a + 3b + 2b = 0 Combine like terms: 3b + 2b = 5b 2a + 5b = 0 Solving 2a + 5b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 2a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 2a + 0 = 0 + -5b 2a = 0 + -5b Remove the zero: 2a = -5b Divide each side by '2'. a = -2.5b Simplifying a = -2.5b
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