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Simplifying 7(5a + b) + 4(3a + 4b) = 0 (5a * 7 + b * 7) + 4(3a + 4b) = 0 (35a + 7b) + 4(3a + 4b) = 0 35a + 7b + (3a * 4 + 4b * 4) = 0 35a + 7b + (12a + 16b) = 0 Reorder the terms: 35a + 12a + 7b + 16b = 0 Combine like terms: 35a + 12a = 47a 47a + 7b + 16b = 0 Combine like terms: 7b + 16b = 23b 47a + 23b = 0 Solving 47a + 23b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-23b' to each side of the equation. 47a + 23b + -23b = 0 + -23b Combine like terms: 23b + -23b = 0 47a + 0 = 0 + -23b 47a = 0 + -23b Remove the zero: 47a = -23b Divide each side by '47'. a = -0.4893617021b Simplifying a = -0.4893617021b
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