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Simplifying 10(9a + 3b) + -7(a + 8b) = 0 (9a * 10 + 3b * 10) + -7(a + 8b) = 0 (90a + 30b) + -7(a + 8b) = 0 90a + 30b + (a * -7 + 8b * -7) = 0 90a + 30b + (-7a + -56b) = 0 Reorder the terms: 90a + -7a + 30b + -56b = 0 Combine like terms: 90a + -7a = 83a 83a + 30b + -56b = 0 Combine like terms: 30b + -56b = -26b 83a + -26b = 0 Solving 83a + -26b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '26b' to each side of the equation. 83a + -26b + 26b = 0 + 26b Combine like terms: -26b + 26b = 0 83a + 0 = 0 + 26b 83a = 0 + 26b Remove the zero: 83a = 26b Divide each side by '83'. a = 0.313253012b Simplifying a = 0.313253012b
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