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Simplifying (2a + -3b + 4c) + -1(-1a + 3b + 4c) = 0 Remove parenthesis around (2a + -3b + 4c) 2a + -3b + 4c + -1(-1a + 3b + 4c) = 0 2a + -3b + 4c + (-1a * -1 + 3b * -1 + 4c * -1) = 0 2a + -3b + 4c + (1a + -3b + -4c) = 0 Reorder the terms: 2a + 1a + -3b + -3b + 4c + -4c = 0 Combine like terms: 2a + 1a = 3a 3a + -3b + -3b + 4c + -4c = 0 Combine like terms: -3b + -3b = -6b 3a + -6b + 4c + -4c = 0 Combine like terms: 4c + -4c = 0 3a + -6b + 0 = 0 3a + -6b = 0 Solving 3a + -6b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6b' to each side of the equation. 3a + -6b + 6b = 0 + 6b Combine like terms: -6b + 6b = 0 3a + 0 = 0 + 6b 3a = 0 + 6b Remove the zero: 3a = 6b Divide each side by '3'. a = 2b Simplifying a = 2b
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