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Simplifying (3a + -4b + -1c) + -1(5a + -2b + 7c) = 0 Remove parenthesis around (3a + -4b + -1c) 3a + -4b + -1c + -1(5a + -2b + 7c) = 0 3a + -4b + -1c + (5a * -1 + -2b * -1 + 7c * -1) = 0 3a + -4b + -1c + (-5a + 2b + -7c) = 0 Reorder the terms: 3a + -5a + -4b + 2b + -1c + -7c = 0 Combine like terms: 3a + -5a = -2a -2a + -4b + 2b + -1c + -7c = 0 Combine like terms: -4b + 2b = -2b -2a + -2b + -1c + -7c = 0 Combine like terms: -1c + -7c = -8c -2a + -2b + -8c = 0 Solving -2a + -2b + -8c = 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. -2a + -2b + 2b + -8c = 0 + 2b Combine like terms: -2b + 2b = 0 -2a + 0 + -8c = 0 + 2b -2a + -8c = 0 + 2b Remove the zero: -2a + -8c = 2b Add '8c' to each side of the equation. -2a + -8c + 8c = 2b + 8c Combine like terms: -8c + 8c = 0 -2a + 0 = 2b + 8c -2a = 2b + 8c Divide each side by '-2'. a = -1b + -4c Simplifying a = -1b + -4c
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