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Simplifying 11(2a + 2b + -4c) + -9(5a + -7b + 2c) = 0 (2a * 11 + 2b * 11 + -4c * 11) + -9(5a + -7b + 2c) = 0 (22a + 22b + -44c) + -9(5a + -7b + 2c) = 0 22a + 22b + -44c + (5a * -9 + -7b * -9 + 2c * -9) = 0 22a + 22b + -44c + (-45a + 63b + -18c) = 0 Reorder the terms: 22a + -45a + 22b + 63b + -44c + -18c = 0 Combine like terms: 22a + -45a = -23a -23a + 22b + 63b + -44c + -18c = 0 Combine like terms: 22b + 63b = 85b -23a + 85b + -44c + -18c = 0 Combine like terms: -44c + -18c = -62c -23a + 85b + -62c = 0 Solving -23a + 85b + -62c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-85b' to each side of the equation. -23a + 85b + -85b + -62c = 0 + -85b Combine like terms: 85b + -85b = 0 -23a + 0 + -62c = 0 + -85b -23a + -62c = 0 + -85b Remove the zero: -23a + -62c = -85b Add '62c' to each side of the equation. -23a + -62c + 62c = -85b + 62c Combine like terms: -62c + 62c = 0 -23a + 0 = -85b + 62c -23a = -85b + 62c Divide each side by '-23'. a = 3.695652174b + -2.695652174c Simplifying a = 3.695652174b + -2.695652174c
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