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Simplifying 8(4a + -1b) + -6(2b + -8a) = 0 (4a * 8 + -1b * 8) + -6(2b + -8a) = 0 (32a + -8b) + -6(2b + -8a) = 0 Reorder the terms: 32a + -8b + -6(-8a + 2b) = 0 32a + -8b + (-8a * -6 + 2b * -6) = 0 32a + -8b + (48a + -12b) = 0 Reorder the terms: 32a + 48a + -8b + -12b = 0 Combine like terms: 32a + 48a = 80a 80a + -8b + -12b = 0 Combine like terms: -8b + -12b = -20b 80a + -20b = 0 Solving 80a + -20b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20b' to each side of the equation. 80a + -20b + 20b = 0 + 20b Combine like terms: -20b + 20b = 0 80a + 0 = 0 + 20b 80a = 0 + 20b Remove the zero: 80a = 20b Divide each side by '80'. a = 0.25b Simplifying a = 0.25b
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