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Simplifying 0.6(18b + 4a) + 0.3(a + -9b + 3) = 0 Reorder the terms: 0.6(4a + 18b) + 0.3(a + -9b + 3) = 0 (4a * 0.6 + 18b * 0.6) + 0.3(a + -9b + 3) = 0 (2.4a + 10.8b) + 0.3(a + -9b + 3) = 0 Reorder the terms: 2.4a + 10.8b + 0.3(3 + a + -9b) = 0 2.4a + 10.8b + (3 * 0.3 + a * 0.3 + -9b * 0.3) = 0 2.4a + 10.8b + (0.9 + 0.3a + -2.7b) = 0 Reorder the terms: 0.9 + 2.4a + 0.3a + 10.8b + -2.7b = 0 Combine like terms: 2.4a + 0.3a = 2.7a 0.9 + 2.7a + 10.8b + -2.7b = 0 Combine like terms: 10.8b + -2.7b = 8.1b 0.9 + 2.7a + 8.1b = 0 Solving 0.9 + 2.7a + 8.1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + 2.7a + -0.9 + 8.1b = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + 2.7a + 8.1b = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + 2.7a + 8.1b = 0 + -0.9 2.7a + 8.1b = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 2.7a + 8.1b = -0.9 Add '-8.1b' to each side of the equation. 2.7a + 8.1b + -8.1b = -0.9 + -8.1b Combine like terms: 8.1b + -8.1b = 0.0 2.7a + 0.0 = -0.9 + -8.1b 2.7a = -0.9 + -8.1b Divide each side by '2.7'. a = -0.3333333333 + -3b Simplifying a = -0.3333333333 + -3b
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