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Simplifying 8(5a + -1b) + -3(7b + -6a) = 0 (5a * 8 + -1b * 8) + -3(7b + -6a) = 0 (40a + -8b) + -3(7b + -6a) = 0 Reorder the terms: 40a + -8b + -3(-6a + 7b) = 0 40a + -8b + (-6a * -3 + 7b * -3) = 0 40a + -8b + (18a + -21b) = 0 Reorder the terms: 40a + 18a + -8b + -21b = 0 Combine like terms: 40a + 18a = 58a 58a + -8b + -21b = 0 Combine like terms: -8b + -21b = -29b 58a + -29b = 0 Solving 58a + -29b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '29b' to each side of the equation. 58a + -29b + 29b = 0 + 29b Combine like terms: -29b + 29b = 0 58a + 0 = 0 + 29b 58a = 0 + 29b Remove the zero: 58a = 29b Divide each side by '58'. a = 0.5b Simplifying a = 0.5b
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