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Simplifying 8(2a + -1b) + -5(4b + -4a) = 0 (2a * 8 + -1b * 8) + -5(4b + -4a) = 0 (16a + -8b) + -5(4b + -4a) = 0 Reorder the terms: 16a + -8b + -5(-4a + 4b) = 0 16a + -8b + (-4a * -5 + 4b * -5) = 0 16a + -8b + (20a + -20b) = 0 Reorder the terms: 16a + 20a + -8b + -20b = 0 Combine like terms: 16a + 20a = 36a 36a + -8b + -20b = 0 Combine like terms: -8b + -20b = -28b 36a + -28b = 0 Solving 36a + -28b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '28b' to each side of the equation. 36a + -28b + 28b = 0 + 28b Combine like terms: -28b + 28b = 0 36a + 0 = 0 + 28b 36a = 0 + 28b Remove the zero: 36a = 28b Divide each side by '36'. a = 0.7777777778b Simplifying a = 0.7777777778b
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