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Simplifying 3(4a + -1b) + -4(2a + -2b) = 0 (4a * 3 + -1b * 3) + -4(2a + -2b) = 0 (12a + -3b) + -4(2a + -2b) = 0 12a + -3b + (2a * -4 + -2b * -4) = 0 12a + -3b + (-8a + 8b) = 0 Reorder the terms: 12a + -8a + -3b + 8b = 0 Combine like terms: 12a + -8a = 4a 4a + -3b + 8b = 0 Combine like terms: -3b + 8b = 5b 4a + 5b = 0 Solving 4a + 5b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 4a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 4a + 0 = 0 + -5b 4a = 0 + -5b Remove the zero: 4a = -5b Divide each side by '4'. a = -1.25b Simplifying a = -1.25b
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