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Simplifying 5(3a + -1b) + -8(7b + -2a) = 0 (3a * 5 + -1b * 5) + -8(7b + -2a) = 0 (15a + -5b) + -8(7b + -2a) = 0 Reorder the terms: 15a + -5b + -8(-2a + 7b) = 0 15a + -5b + (-2a * -8 + 7b * -8) = 0 15a + -5b + (16a + -56b) = 0 Reorder the terms: 15a + 16a + -5b + -56b = 0 Combine like terms: 15a + 16a = 31a 31a + -5b + -56b = 0 Combine like terms: -5b + -56b = -61b 31a + -61b = 0 Solving 31a + -61b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '61b' to each side of the equation. 31a + -61b + 61b = 0 + 61b Combine like terms: -61b + 61b = 0 31a + 0 = 0 + 61b 31a = 0 + 61b Remove the zero: 31a = 61b Divide each side by '31'. a = 1.967741935b Simplifying a = 1.967741935b
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