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Simplifying 8(2a + -3b) + -5(6b + -4a) = 0 (2a * 8 + -3b * 8) + -5(6b + -4a) = 0 (16a + -24b) + -5(6b + -4a) = 0 Reorder the terms: 16a + -24b + -5(-4a + 6b) = 0 16a + -24b + (-4a * -5 + 6b * -5) = 0 16a + -24b + (20a + -30b) = 0 Reorder the terms: 16a + 20a + -24b + -30b = 0 Combine like terms: 16a + 20a = 36a 36a + -24b + -30b = 0 Combine like terms: -24b + -30b = -54b 36a + -54b = 0 Solving 36a + -54b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '54b' to each side of the equation. 36a + -54b + 54b = 0 + 54b Combine like terms: -54b + 54b = 0 36a + 0 = 0 + 54b 36a = 0 + 54b Remove the zero: 36a = 54b Divide each side by '36'. a = 1.5b Simplifying a = 1.5b
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