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Simplifying 11(-2a + 2b + -3c) + -9(3a + -5b + 3a) = 0 (-2a * 11 + 2b * 11 + -3c * 11) + -9(3a + -5b + 3a) = 0 (-22a + 22b + -33c) + -9(3a + -5b + 3a) = 0 Reorder the terms: -22a + 22b + -33c + -9(3a + 3a + -5b) = 0 Combine like terms: 3a + 3a = 6a -22a + 22b + -33c + -9(6a + -5b) = 0 -22a + 22b + -33c + (6a * -9 + -5b * -9) = 0 -22a + 22b + -33c + (-54a + 45b) = 0 Reorder the terms: -22a + -54a + 22b + 45b + -33c = 0 Combine like terms: -22a + -54a = -76a -76a + 22b + 45b + -33c = 0 Combine like terms: 22b + 45b = 67b -76a + 67b + -33c = 0 Solving -76a + 67b + -33c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-67b' to each side of the equation. -76a + 67b + -67b + -33c = 0 + -67b Combine like terms: 67b + -67b = 0 -76a + 0 + -33c = 0 + -67b -76a + -33c = 0 + -67b Remove the zero: -76a + -33c = -67b Add '33c' to each side of the equation. -76a + -33c + 33c = -67b + 33c Combine like terms: -33c + 33c = 0 -76a + 0 = -67b + 33c -76a = -67b + 33c Divide each side by '-76'. a = 0.8815789474b + -0.4342105263c Simplifying a = 0.8815789474b + -0.4342105263c
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