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Simplifying 7(5a + -1b) + -4(3b + -4a) = 0 (5a * 7 + -1b * 7) + -4(3b + -4a) = 0 (35a + -7b) + -4(3b + -4a) = 0 Reorder the terms: 35a + -7b + -4(-4a + 3b) = 0 35a + -7b + (-4a * -4 + 3b * -4) = 0 35a + -7b + (16a + -12b) = 0 Reorder the terms: 35a + 16a + -7b + -12b = 0 Combine like terms: 35a + 16a = 51a 51a + -7b + -12b = 0 Combine like terms: -7b + -12b = -19b 51a + -19b = 0 Solving 51a + -19b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '19b' to each side of the equation. 51a + -19b + 19b = 0 + 19b Combine like terms: -19b + 19b = 0 51a + 0 = 0 + 19b 51a = 0 + 19b Remove the zero: 51a = 19b Divide each side by '51'. a = 0.3725490196b Simplifying a = 0.3725490196b
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