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Simplifying 7(5a + -1b) + -5(6b + -6a) = 0 (5a * 7 + -1b * 7) + -5(6b + -6a) = 0 (35a + -7b) + -5(6b + -6a) = 0 Reorder the terms: 35a + -7b + -5(-6a + 6b) = 0 35a + -7b + (-6a * -5 + 6b * -5) = 0 35a + -7b + (30a + -30b) = 0 Reorder the terms: 35a + 30a + -7b + -30b = 0 Combine like terms: 35a + 30a = 65a 65a + -7b + -30b = 0 Combine like terms: -7b + -30b = -37b 65a + -37b = 0 Solving 65a + -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. 65a + -37b + 37b = 0 + 37b Combine like terms: -37b + 37b = 0 65a + 0 = 0 + 37b 65a = 0 + 37b Remove the zero: 65a = 37b Divide each side by '65'. a = 0.5692307692b Simplifying a = 0.5692307692b
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