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Simplifying 3(2a + -1b) + -1(5b + -3a) = 0 (2a * 3 + -1b * 3) + -1(5b + -3a) = 0 (6a + -3b) + -1(5b + -3a) = 0 Reorder the terms: 6a + -3b + -1(-3a + 5b) = 0 6a + -3b + (-3a * -1 + 5b * -1) = 0 6a + -3b + (3a + -5b) = 0 Reorder the terms: 6a + 3a + -3b + -5b = 0 Combine like terms: 6a + 3a = 9a 9a + -3b + -5b = 0 Combine like terms: -3b + -5b = -8b 9a + -8b = 0 Solving 9a + -8b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8b' to each side of the equation. 9a + -8b + 8b = 0 + 8b Combine like terms: -8b + 8b = 0 9a + 0 = 0 + 8b 9a = 0 + 8b Remove the zero: 9a = 8b Divide each side by '9'. a = 0.8888888889b Simplifying a = 0.8888888889b
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