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Simplifying 4(2a + -1b) + -6(3b + -7a) = 0 (2a * 4 + -1b * 4) + -6(3b + -7a) = 0 (8a + -4b) + -6(3b + -7a) = 0 Reorder the terms: 8a + -4b + -6(-7a + 3b) = 0 8a + -4b + (-7a * -6 + 3b * -6) = 0 8a + -4b + (42a + -18b) = 0 Reorder the terms: 8a + 42a + -4b + -18b = 0 Combine like terms: 8a + 42a = 50a 50a + -4b + -18b = 0 Combine like terms: -4b + -18b = -22b 50a + -22b = 0 Solving 50a + -22b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '22b' to each side of the equation. 50a + -22b + 22b = 0 + 22b Combine like terms: -22b + 22b = 0 50a + 0 = 0 + 22b 50a = 0 + 22b Remove the zero: 50a = 22b Divide each side by '50'. a = 0.44b Simplifying a = 0.44b
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