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Simplifying 8(4a + 9b) + -5(a + 7b) = 0 (4a * 8 + 9b * 8) + -5(a + 7b) = 0 (32a + 72b) + -5(a + 7b) = 0 32a + 72b + (a * -5 + 7b * -5) = 0 32a + 72b + (-5a + -35b) = 0 Reorder the terms: 32a + -5a + 72b + -35b = 0 Combine like terms: 32a + -5a = 27a 27a + 72b + -35b = 0 Combine like terms: 72b + -35b = 37b 27a + 37b = 0 Solving 27a + 37b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-37b' to each side of the equation. 27a + 37b + -37b = 0 + -37b Combine like terms: 37b + -37b = 0 27a + 0 = 0 + -37b 27a = 0 + -37b Remove the zero: 27a = -37b Divide each side by '27'. a = -1.37037037b Simplifying a = -1.37037037b
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