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Simplifying 3(8a + -1b) + -8(2b + -5a) = 0 (8a * 3 + -1b * 3) + -8(2b + -5a) = 0 (24a + -3b) + -8(2b + -5a) = 0 Reorder the terms: 24a + -3b + -8(-5a + 2b) = 0 24a + -3b + (-5a * -8 + 2b * -8) = 0 24a + -3b + (40a + -16b) = 0 Reorder the terms: 24a + 40a + -3b + -16b = 0 Combine like terms: 24a + 40a = 64a 64a + -3b + -16b = 0 Combine like terms: -3b + -16b = -19b 64a + -19b = 0 Solving 64a + -19b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '19b' to each side of the equation. 64a + -19b + 19b = 0 + 19b Combine like terms: -19b + 19b = 0 64a + 0 = 0 + 19b 64a = 0 + 19b Remove the zero: 64a = 19b Divide each side by '64'. a = 0.296875b Simplifying a = 0.296875b
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