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Simplifying 5(3a + -3b) + 4(a + -4b) = 0 (3a * 5 + -3b * 5) + 4(a + -4b) = 0 (15a + -15b) + 4(a + -4b) = 0 15a + -15b + (a * 4 + -4b * 4) = 0 15a + -15b + (4a + -16b) = 0 Reorder the terms: 15a + 4a + -15b + -16b = 0 Combine like terms: 15a + 4a = 19a 19a + -15b + -16b = 0 Combine like terms: -15b + -16b = -31b 19a + -31b = 0 Solving 19a + -31b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '31b' to each side of the equation. 19a + -31b + 31b = 0 + 31b Combine like terms: -31b + 31b = 0 19a + 0 = 0 + 31b 19a = 0 + 31b Remove the zero: 19a = 31b Divide each side by '19'. a = 1.631578947b Simplifying a = 1.631578947b
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