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Simplifying -3(1 + -14b) + 12(1 + 7b) = -117 (1 * -3 + -14b * -3) + 12(1 + 7b) = -117 (-3 + 42b) + 12(1 + 7b) = -117 -3 + 42b + (1 * 12 + 7b * 12) = -117 -3 + 42b + (12 + 84b) = -117 Reorder the terms: -3 + 12 + 42b + 84b = -117 Combine like terms: -3 + 12 = 9 9 + 42b + 84b = -117 Combine like terms: 42b + 84b = 126b 9 + 126b = -117 Solving 9 + 126b = -117 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 126b = -117 + -9 Combine like terms: 9 + -9 = 0 0 + 126b = -117 + -9 126b = -117 + -9 Combine like terms: -117 + -9 = -126 126b = -126 Divide each side by '126'. b = -1 Simplifying b = -1
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