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Simplifying 5(a + -1b) + -2(a + -1b) + 8(a + -1b) = 0 (a * 5 + -1b * 5) + -2(a + -1b) + 8(a + -1b) = 0 (5a + -5b) + -2(a + -1b) + 8(a + -1b) = 0 5a + -5b + (a * -2 + -1b * -2) + 8(a + -1b) = 0 5a + -5b + (-2a + 2b) + 8(a + -1b) = 0 5a + -5b + -2a + 2b + (a * 8 + -1b * 8) = 0 5a + -5b + -2a + 2b + (8a + -8b) = 0 Reorder the terms: 5a + -2a + 8a + -5b + 2b + -8b = 0 Combine like terms: 5a + -2a = 3a 3a + 8a + -5b + 2b + -8b = 0 Combine like terms: 3a + 8a = 11a 11a + -5b + 2b + -8b = 0 Combine like terms: -5b + 2b = -3b 11a + -3b + -8b = 0 Combine like terms: -3b + -8b = -11b 11a + -11b = 0 Solving 11a + -11b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11b' to each side of the equation. 11a + -11b + 11b = 0 + 11b Combine like terms: -11b + 11b = 0 11a + 0 = 0 + 11b 11a = 0 + 11b Remove the zero: 11a = 11b Divide each side by '11'. a = b Simplifying a = b
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