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Simplifying 2(a + b) + 3(2a + -1b) = 0 (a * 2 + b * 2) + 3(2a + -1b) = 0 (2a + 2b) + 3(2a + -1b) = 0 2a + 2b + (2a * 3 + -1b * 3) = 0 2a + 2b + (6a + -3b) = 0 Reorder the terms: 2a + 6a + 2b + -3b = 0 Combine like terms: 2a + 6a = 8a 8a + 2b + -3b = 0 Combine like terms: 2b + -3b = -1b 8a + -1b = 0 Solving 8a + -1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 8a + -1b + b = 0 + b Combine like terms: -1b + b = 0 8a + 0 = 0 + b 8a = 0 + b Remove the zero: 8a = b Divide each side by '8'. a = 0.125b Simplifying a = 0.125b
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