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Simplifying 2(4a + -1b) + -5(4b + -2a) = 0 (4a * 2 + -1b * 2) + -5(4b + -2a) = 0 (8a + -2b) + -5(4b + -2a) = 0 Reorder the terms: 8a + -2b + -5(-2a + 4b) = 0 8a + -2b + (-2a * -5 + 4b * -5) = 0 8a + -2b + (10a + -20b) = 0 Reorder the terms: 8a + 10a + -2b + -20b = 0 Combine like terms: 8a + 10a = 18a 18a + -2b + -20b = 0 Combine like terms: -2b + -20b = -22b 18a + -22b = 0 Solving 18a + -22b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '22b' to each side of the equation. 18a + -22b + 22b = 0 + 22b Combine like terms: -22b + 22b = 0 18a + 0 = 0 + 22b 18a = 0 + 22b Remove the zero: 18a = 22b Divide each side by '18'. a = 1.222222222b Simplifying a = 1.222222222b
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