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Simplifying (8.1a + -4b + 0.9c) + -1(2.6a + -5.6b + 2.8c) = 0 Remove parenthesis around (8.1a + -4b + 0.9c) 8.1a + -4b + 0.9c + -1(2.6a + -5.6b + 2.8c) = 0 8.1a + -4b + 0.9c + (2.6a * -1 + -5.6b * -1 + 2.8c * -1) = 0 8.1a + -4b + 0.9c + (-2.6a + 5.6b + -2.8c) = 0 Reorder the terms: 8.1a + -2.6a + -4b + 5.6b + 0.9c + -2.8c = 0 Combine like terms: 8.1a + -2.6a = 5.5a 5.5a + -4b + 5.6b + 0.9c + -2.8c = 0 Combine like terms: -4b + 5.6b = 1.6b 5.5a + 1.6b + 0.9c + -2.8c = 0 Combine like terms: 0.9c + -2.8c = -1.9c 5.5a + 1.6b + -1.9c = 0 Solving 5.5a + 1.6b + -1.9c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.6b' to each side of the equation. 5.5a + 1.6b + -1.6b + -1.9c = 0 + -1.6b Combine like terms: 1.6b + -1.6b = 0.0 5.5a + 0.0 + -1.9c = 0 + -1.6b 5.5a + -1.9c = 0 + -1.6b Remove the zero: 5.5a + -1.9c = -1.6b Add '1.9c' to each side of the equation. 5.5a + -1.9c + 1.9c = -1.6b + 1.9c Combine like terms: -1.9c + 1.9c = 0.0 5.5a + 0.0 = -1.6b + 1.9c 5.5a = -1.6b + 1.9c Divide each side by '5.5'. a = -0.2909090909b + 0.3454545455c Simplifying a = -0.2909090909b + 0.3454545455c
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