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Simplifying 5(a + -2b) + -3(a + -3b) = 0 (a * 5 + -2b * 5) + -3(a + -3b) = 0 (5a + -10b) + -3(a + -3b) = 0 5a + -10b + (a * -3 + -3b * -3) = 0 5a + -10b + (-3a + 9b) = 0 Reorder the terms: 5a + -3a + -10b + 9b = 0 Combine like terms: 5a + -3a = 2a 2a + -10b + 9b = 0 Combine like terms: -10b + 9b = -1b 2a + -1b = 0 Solving 2a + -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. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5b
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