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Simplifying 11(-3a + 2b + -4c) + -8(3a + -6b + 2c) = 0 (-3a * 11 + 2b * 11 + -4c * 11) + -8(3a + -6b + 2c) = 0 (-33a + 22b + -44c) + -8(3a + -6b + 2c) = 0 -33a + 22b + -44c + (3a * -8 + -6b * -8 + 2c * -8) = 0 -33a + 22b + -44c + (-24a + 48b + -16c) = 0 Reorder the terms: -33a + -24a + 22b + 48b + -44c + -16c = 0 Combine like terms: -33a + -24a = -57a -57a + 22b + 48b + -44c + -16c = 0 Combine like terms: 22b + 48b = 70b -57a + 70b + -44c + -16c = 0 Combine like terms: -44c + -16c = -60c -57a + 70b + -60c = 0 Solving -57a + 70b + -60c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-70b' to each side of the equation. -57a + 70b + -70b + -60c = 0 + -70b Combine like terms: 70b + -70b = 0 -57a + 0 + -60c = 0 + -70b -57a + -60c = 0 + -70b Remove the zero: -57a + -60c = -70b Add '60c' to each side of the equation. -57a + -60c + 60c = -70b + 60c Combine like terms: -60c + 60c = 0 -57a + 0 = -70b + 60c -57a = -70b + 60c Divide each side by '-57'. a = 1.228070175b + -1.052631579c Simplifying a = 1.228070175b + -1.052631579c
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