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Simplifying 0.3(3a + 2b) + 0.05(8b + 2a) = 0 (3a * 0.3 + 2b * 0.3) + 0.05(8b + 2a) = 0 (0.9a + 0.6b) + 0.05(8b + 2a) = 0 Reorder the terms: 0.9a + 0.6b + 0.05(2a + 8b) = 0 0.9a + 0.6b + (2a * 0.05 + 8b * 0.05) = 0 0.9a + 0.6b + (0.1a + 0.4b) = 0 Reorder the terms: 0.9a + 0.1a + 0.6b + 0.4b = 0 Combine like terms: 0.9a + 0.1a = 1a 1a + 0.6b + 0.4b = 0 Combine like terms: 0.6b + 0.4b = 1b 1a + 1b = 0 Solving 1a + 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. 1a + 1b + -1b = 0 + -1b Combine like terms: 1b + -1b = 0 1a + 0 = 0 + -1b 1a = 0 + -1b Remove the zero: 1a = -1b Divide each side by '1'. a = -1b Simplifying a = -1b
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