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Simplifying 5(2a + b) + 2(a + 2b) + -5(2a + 2b) = 0 (2a * 5 + b * 5) + 2(a + 2b) + -5(2a + 2b) = 0 (10a + 5b) + 2(a + 2b) + -5(2a + 2b) = 0 10a + 5b + (a * 2 + 2b * 2) + -5(2a + 2b) = 0 10a + 5b + (2a + 4b) + -5(2a + 2b) = 0 10a + 5b + 2a + 4b + (2a * -5 + 2b * -5) = 0 10a + 5b + 2a + 4b + (-10a + -10b) = 0 Reorder the terms: 10a + 2a + -10a + 5b + 4b + -10b = 0 Combine like terms: 10a + 2a = 12a 12a + -10a + 5b + 4b + -10b = 0 Combine like terms: 12a + -10a = 2a 2a + 5b + 4b + -10b = 0 Combine like terms: 5b + 4b = 9b 2a + 9b + -10b = 0 Combine like terms: 9b + -10b = -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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