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Simplifying [-2(3a + -9b) + -1(-5a + 7b)] + -2a + -6b = 0 [(3a * -2 + -9b * -2) + -1(-5a + 7b)] + -2a + -6b = 0 [(-6a + 18b) + -1(-5a + 7b)] + -2a + -6b = 0 [-6a + 18b + (-5a * -1 + 7b * -1)] + -2a + -6b = 0 [-6a + 18b + (5a + -7b)] + -2a + -6b = 0 Reorder the terms: [-6a + 5a + 18b + -7b] + -2a + -6b = 0 Combine like terms: -6a + 5a = -1a [-1a + 18b + -7b] + -2a + -6b = 0 Combine like terms: 18b + -7b = 11b [-1a + 11b] + -2a + -6b = 0 Remove brackets around [-1a + 11b] -1a + 11b + -2a + -6b = 0 Reorder the terms: -1a + -2a + 11b + -6b = 0 Combine like terms: -1a + -2a = -3a -3a + 11b + -6b = 0 Combine like terms: 11b + -6b = 5b -3a + 5b = 0 Solving -3a + 5b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. -3a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 -3a + 0 = 0 + -5b -3a = 0 + -5b Remove the zero: -3a = -5b Divide each side by '-3'. a = 1.666666667b Simplifying a = 1.666666667b
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