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Simplifying 6(5a + -1b) + -6(7b + -7a) = 0 (5a * 6 + -1b * 6) + -6(7b + -7a) = 0 (30a + -6b) + -6(7b + -7a) = 0 Reorder the terms: 30a + -6b + -6(-7a + 7b) = 0 30a + -6b + (-7a * -6 + 7b * -6) = 0 30a + -6b + (42a + -42b) = 0 Reorder the terms: 30a + 42a + -6b + -42b = 0 Combine like terms: 30a + 42a = 72a 72a + -6b + -42b = 0 Combine like terms: -6b + -42b = -48b 72a + -48b = 0 Solving 72a + -48b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '48b' to each side of the equation. 72a + -48b + 48b = 0 + 48b Combine like terms: -48b + 48b = 0 72a + 0 = 0 + 48b 72a = 0 + 48b Remove the zero: 72a = 48b Divide each side by '72'. a = 0.6666666667b Simplifying a = 0.6666666667b
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