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Simplifying 5(a + b) + -2(a + b) + -1(a + -1b) = 0 (a * 5 + b * 5) + -2(a + b) + -1(a + -1b) = 0 (5a + 5b) + -2(a + b) + -1(a + -1b) = 0 5a + 5b + (a * -2 + b * -2) + -1(a + -1b) = 0 5a + 5b + (-2a + -2b) + -1(a + -1b) = 0 5a + 5b + -2a + -2b + (a * -1 + -1b * -1) = 0 5a + 5b + -2a + -2b + (-1a + 1b) = 0 Reorder the terms: 5a + -2a + -1a + 5b + -2b + 1b = 0 Combine like terms: 5a + -2a = 3a 3a + -1a + 5b + -2b + 1b = 0 Combine like terms: 3a + -1a = 2a 2a + 5b + -2b + 1b = 0 Combine like terms: 5b + -2b = 3b 2a + 3b + 1b = 0 Combine like terms: 3b + 1b = 4b 2a + 4b = 0 Solving 2a + 4b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 2a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 2a + 0 = 0 + -4b 2a = 0 + -4b Remove the zero: 2a = -4b Divide each side by '2'. a = -2b Simplifying a = -2b
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