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Simplifying 5(2a + 4b) + -9(a + 7b) = 0 (2a * 5 + 4b * 5) + -9(a + 7b) = 0 (10a + 20b) + -9(a + 7b) = 0 10a + 20b + (a * -9 + 7b * -9) = 0 10a + 20b + (-9a + -63b) = 0 Reorder the terms: 10a + -9a + 20b + -63b = 0 Combine like terms: 10a + -9a = 1a 1a + 20b + -63b = 0 Combine like terms: 20b + -63b = -43b 1a + -43b = 0 Solving 1a + -43b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '43b' to each side of the equation. 1a + -43b + 43b = 0 + 43b Combine like terms: -43b + 43b = 0 1a + 0 = 0 + 43b 1a = 0 + 43b Remove the zero: 1a = 43b Divide each side by '1'. a = 43b Simplifying a = 43b
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