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Simplifying 5(a + -1b) + 2(2a + 3b) = 0 (a * 5 + -1b * 5) + 2(2a + 3b) = 0 (5a + -5b) + 2(2a + 3b) = 0 5a + -5b + (2a * 2 + 3b * 2) = 0 5a + -5b + (4a + 6b) = 0 Reorder the terms: 5a + 4a + -5b + 6b = 0 Combine like terms: 5a + 4a = 9a 9a + -5b + 6b = 0 Combine like terms: -5b + 6b = 1b 9a + 1b = 0 Solving 9a + 1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 9a + 1b + -1b = 0 + -1b Combine like terms: 1b + -1b = 0 9a + 0 = 0 + -1b 9a = 0 + -1b Remove the zero: 9a = -1b Divide each side by '9'. a = -0.1111111111b Simplifying a = -0.1111111111b
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