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Simplifying 5(a + 3b) + -3(a + -1b) = 0 (a * 5 + 3b * 5) + -3(a + -1b) = 0 (5a + 15b) + -3(a + -1b) = 0 5a + 15b + (a * -3 + -1b * -3) = 0 5a + 15b + (-3a + 3b) = 0 Reorder the terms: 5a + -3a + 15b + 3b = 0 Combine like terms: 5a + -3a = 2a 2a + 15b + 3b = 0 Combine like terms: 15b + 3b = 18b 2a + 18b = 0 Solving 2a + 18b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-18b' to each side of the equation. 2a + 18b + -18b = 0 + -18b Combine like terms: 18b + -18b = 0 2a + 0 = 0 + -18b 2a = 0 + -18b Remove the zero: 2a = -18b Divide each side by '2'. a = -9b Simplifying a = -9b
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