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Simplifying 5(a + b) + 2(a + c) + -4(b + c) = 0 (a * 5 + b * 5) + 2(a + c) + -4(b + c) = 0 (5a + 5b) + 2(a + c) + -4(b + c) = 0 5a + 5b + (a * 2 + c * 2) + -4(b + c) = 0 5a + 5b + (2a + 2c) + -4(b + c) = 0 5a + 5b + 2a + 2c + (b * -4 + c * -4) = 0 5a + 5b + 2a + 2c + (-4b + -4c) = 0 Reorder the terms: 5a + 2a + 5b + -4b + 2c + -4c = 0 Combine like terms: 5a + 2a = 7a 7a + 5b + -4b + 2c + -4c = 0 Combine like terms: 5b + -4b = 1b 7a + 1b + 2c + -4c = 0 Combine like terms: 2c + -4c = -2c 7a + 1b + -2c = 0 Solving 7a + 1b + -2c = 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. 7a + 1b + -1b + -2c = 0 + -1b Combine like terms: 1b + -1b = 0 7a + 0 + -2c = 0 + -1b 7a + -2c = 0 + -1b Remove the zero: 7a + -2c = -1b Add '2c' to each side of the equation. 7a + -2c + 2c = -1b + 2c Combine like terms: -2c + 2c = 0 7a + 0 = -1b + 2c 7a = -1b + 2c Divide each side by '7'. a = -0.1428571429b + 0.2857142857c Simplifying a = -0.1428571429b + 0.2857142857c
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