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Simplifying 5a + 5b + 5c + -1(3a + 4b + -2c) = 0 5a + 5b + 5c + (3a * -1 + 4b * -1 + -2c * -1) = 0 5a + 5b + 5c + (-3a + -4b + 2c) = 0 Reorder the terms: 5a + -3a + 5b + -4b + 5c + 2c = 0 Combine like terms: 5a + -3a = 2a 2a + 5b + -4b + 5c + 2c = 0 Combine like terms: 5b + -4b = 1b 2a + 1b + 5c + 2c = 0 Combine like terms: 5c + 2c = 7c 2a + 1b + 7c = 0 Solving 2a + 1b + 7c = 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. 2a + 1b + -1b + 7c = 0 + -1b Combine like terms: 1b + -1b = 0 2a + 0 + 7c = 0 + -1b 2a + 7c = 0 + -1b Remove the zero: 2a + 7c = -1b Add '-7c' to each side of the equation. 2a + 7c + -7c = -1b + -7c Combine like terms: 7c + -7c = 0 2a + 0 = -1b + -7c 2a = -1b + -7c Divide each side by '2'. a = -0.5b + -3.5c Simplifying a = -0.5b + -3.5c
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