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Simplifying -5(a + -1b) + -1(a + -1b) + 8(a + -1b) = 0 (a * -5 + -1b * -5) + -1(a + -1b) + 8(a + -1b) = 0 (-5a + 5b) + -1(a + -1b) + 8(a + -1b) = 0 -5a + 5b + (a * -1 + -1b * -1) + 8(a + -1b) = 0 -5a + 5b + (-1a + 1b) + 8(a + -1b) = 0 -5a + 5b + -1a + 1b + (a * 8 + -1b * 8) = 0 -5a + 5b + -1a + 1b + (8a + -8b) = 0 Reorder the terms: -5a + -1a + 8a + 5b + 1b + -8b = 0 Combine like terms: -5a + -1a = -6a -6a + 8a + 5b + 1b + -8b = 0 Combine like terms: -6a + 8a = 2a 2a + 5b + 1b + -8b = 0 Combine like terms: 5b + 1b = 6b 2a + 6b + -8b = 0 Combine like terms: 6b + -8b = -2b 2a + -2b = 0 Solving 2a + -2b = 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 = 0 + 2b Combine like terms: -2b + 2b = 0 2a + 0 = 0 + 2b 2a = 0 + 2b Remove the zero: 2a = 2b Divide each side by '2'. a = b Simplifying a = b
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