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Simplifying 11(-2a + 3b + -3c) + -8(4a + -7b + 2c) = 0 (-2a * 11 + 3b * 11 + -3c * 11) + -8(4a + -7b + 2c) = 0 (-22a + 33b + -33c) + -8(4a + -7b + 2c) = 0 -22a + 33b + -33c + (4a * -8 + -7b * -8 + 2c * -8) = 0 -22a + 33b + -33c + (-32a + 56b + -16c) = 0 Reorder the terms: -22a + -32a + 33b + 56b + -33c + -16c = 0 Combine like terms: -22a + -32a = -54a -54a + 33b + 56b + -33c + -16c = 0 Combine like terms: 33b + 56b = 89b -54a + 89b + -33c + -16c = 0 Combine like terms: -33c + -16c = -49c -54a + 89b + -49c = 0 Solving -54a + 89b + -49c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-89b' to each side of the equation. -54a + 89b + -89b + -49c = 0 + -89b Combine like terms: 89b + -89b = 0 -54a + 0 + -49c = 0 + -89b -54a + -49c = 0 + -89b Remove the zero: -54a + -49c = -89b Add '49c' to each side of the equation. -54a + -49c + 49c = -89b + 49c Combine like terms: -49c + 49c = 0 -54a + 0 = -89b + 49c -54a = -89b + 49c Divide each side by '-54'. a = 1.648148148b + -0.9074074074c Simplifying a = 1.648148148b + -0.9074074074c
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