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Simplifying 2(a + -1b) + 3(a + -1b) + -4(a + -1b) = 0 (a * 2 + -1b * 2) + 3(a + -1b) + -4(a + -1b) = 0 (2a + -2b) + 3(a + -1b) + -4(a + -1b) = 0 2a + -2b + (a * 3 + -1b * 3) + -4(a + -1b) = 0 2a + -2b + (3a + -3b) + -4(a + -1b) = 0 2a + -2b + 3a + -3b + (a * -4 + -1b * -4) = 0 2a + -2b + 3a + -3b + (-4a + 4b) = 0 Reorder the terms: 2a + 3a + -4a + -2b + -3b + 4b = 0 Combine like terms: 2a + 3a = 5a 5a + -4a + -2b + -3b + 4b = 0 Combine like terms: 5a + -4a = 1a 1a + -2b + -3b + 4b = 0 Combine like terms: -2b + -3b = -5b 1a + -5b + 4b = 0 Combine like terms: -5b + 4b = -1b 1a + -1b = 0 Solving 1a + -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. 1a + -1b + b = 0 + b Combine like terms: -1b + b = 0 1a + 0 = 0 + b 1a = 0 + b Remove the zero: 1a = b Divide each side by '1'. a = b Simplifying a = b
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