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Simplifying 0.5(b + a + 1) + 0.5(b + -1a + 1) = 0 Reorder the terms: 0.5(1 + a + b) + 0.5(b + -1a + 1) = 0 (1 * 0.5 + a * 0.5 + b * 0.5) + 0.5(b + -1a + 1) = 0 (0.5 + 0.5a + 0.5b) + 0.5(b + -1a + 1) = 0 Reorder the terms: 0.5 + 0.5a + 0.5b + 0.5(1 + -1a + b) = 0 0.5 + 0.5a + 0.5b + (1 * 0.5 + -1a * 0.5 + b * 0.5) = 0 0.5 + 0.5a + 0.5b + (0.5 + -0.5a + 0.5b) = 0 Reorder the terms: 0.5 + 0.5 + 0.5a + -0.5a + 0.5b + 0.5b = 0 Combine like terms: 0.5 + 0.5 = 1 1 + 0.5a + -0.5a + 0.5b + 0.5b = 0 Combine like terms: 0.5a + -0.5a = 0.0 1 + 0.0 + 0.5b + 0.5b = 0 1 + 0.5b + 0.5b = 0 Combine like terms: 0.5b + 0.5b = 1b 1 + 1b = 0 Solving 1 + 1b = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1b = 0 + -1 1b = 0 + -1 Combine like terms: 0 + -1 = -1 1b = -1 Divide each side by '1'. b = -1 Simplifying b = -1
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