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Simplifying 4a + -1b + -4(a + -1b) + 2(a + -2b) = 0 4a + -1b + (a * -4 + -1b * -4) + 2(a + -2b) = 0 4a + -1b + (-4a + 4b) + 2(a + -2b) = 0 4a + -1b + -4a + 4b + (a * 2 + -2b * 2) = 0 4a + -1b + -4a + 4b + (2a + -4b) = 0 Reorder the terms: 4a + -4a + 2a + -1b + 4b + -4b = 0 Combine like terms: 4a + -4a = 0 0 + 2a + -1b + 4b + -4b = 0 2a + -1b + 4b + -4b = 0 Combine like terms: -1b + 4b = 3b 2a + 3b + -4b = 0 Combine like terms: 3b + -4b = -1b 2a + -1b = 0 Solving 2a + -1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5b
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