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Simplifying 3(a + -1b) + -1(a + -1b) + 8(a + -1b) = 0 (a * 3 + -1b * 3) + -1(a + -1b) + 8(a + -1b) = 0 (3a + -3b) + -1(a + -1b) + 8(a + -1b) = 0 3a + -3b + (a * -1 + -1b * -1) + 8(a + -1b) = 0 3a + -3b + (-1a + 1b) + 8(a + -1b) = 0 3a + -3b + -1a + 1b + (a * 8 + -1b * 8) = 0 3a + -3b + -1a + 1b + (8a + -8b) = 0 Reorder the terms: 3a + -1a + 8a + -3b + 1b + -8b = 0 Combine like terms: 3a + -1a = 2a 2a + 8a + -3b + 1b + -8b = 0 Combine like terms: 2a + 8a = 10a 10a + -3b + 1b + -8b = 0 Combine like terms: -3b + 1b = -2b 10a + -2b + -8b = 0 Combine like terms: -2b + -8b = -10b 10a + -10b = 0 Solving 10a + -10b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10b' to each side of the equation. 10a + -10b + 10b = 0 + 10b Combine like terms: -10b + 10b = 0 10a + 0 = 0 + 10b 10a = 0 + 10b Remove the zero: 10a = 10b Divide each side by '10'. a = b Simplifying a = b
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