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Simplifying (4a + -3b + 7c) + (3a + b + -23c) = 0 Remove parenthesis around (4a + -3b + 7c) 4a + -3b + 7c + (3a + b + -23c) = 0 Remove parenthesis around (3a + b + -23c) 4a + -3b + 7c + 3a + b + -23c = 0 Reorder the terms: 4a + 3a + -3b + b + 7c + -23c = 0 Combine like terms: 4a + 3a = 7a 7a + -3b + b + 7c + -23c = 0 Combine like terms: -3b + b = -2b 7a + -2b + 7c + -23c = 0 Combine like terms: 7c + -23c = -16c 7a + -2b + -16c = 0 Solving 7a + -2b + -16c = 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. 7a + -2b + 2b + -16c = 0 + 2b Combine like terms: -2b + 2b = 0 7a + 0 + -16c = 0 + 2b 7a + -16c = 0 + 2b Remove the zero: 7a + -16c = 2b Add '16c' to each side of the equation. 7a + -16c + 16c = 2b + 16c Combine like terms: -16c + 16c = 0 7a + 0 = 2b + 16c 7a = 2b + 16c Divide each side by '7'. a = 0.2857142857b + 2.285714286c Simplifying a = 0.2857142857b + 2.285714286c
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