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Simplifying (2a + -3b + -1c) + (a + 5b + 3c) = 0 Remove parenthesis around (2a + -3b + -1c) 2a + -3b + -1c + (a + 5b + 3c) = 0 Remove parenthesis around (a + 5b + 3c) 2a + -3b + -1c + a + 5b + 3c = 0 Reorder the terms: 2a + a + -3b + 5b + -1c + 3c = 0 Combine like terms: 2a + a = 3a 3a + -3b + 5b + -1c + 3c = 0 Combine like terms: -3b + 5b = 2b 3a + 2b + -1c + 3c = 0 Combine like terms: -1c + 3c = 2c 3a + 2b + 2c = 0 Solving 3a + 2b + 2c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -2b + 2c = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 + 2c = 0 + -2b 3a + 2c = 0 + -2b Remove the zero: 3a + 2c = -2b Add '-2c' to each side of the equation. 3a + 2c + -2c = -2b + -2c Combine like terms: 2c + -2c = 0 3a + 0 = -2b + -2c 3a = -2b + -2c Divide each side by '3'. a = -0.6666666667b + -0.6666666667c Simplifying a = -0.6666666667b + -0.6666666667c
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