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Simplifying -2b + 8 + 4b + -6 = 3(3b + 4) + 7(2b + 5) Reorder the terms: 8 + -6 + -2b + 4b = 3(3b + 4) + 7(2b + 5) Combine like terms: 8 + -6 = 2 2 + -2b + 4b = 3(3b + 4) + 7(2b + 5) Combine like terms: -2b + 4b = 2b 2 + 2b = 3(3b + 4) + 7(2b + 5) Reorder the terms: 2 + 2b = 3(4 + 3b) + 7(2b + 5) 2 + 2b = (4 * 3 + 3b * 3) + 7(2b + 5) 2 + 2b = (12 + 9b) + 7(2b + 5) Reorder the terms: 2 + 2b = 12 + 9b + 7(5 + 2b) 2 + 2b = 12 + 9b + (5 * 7 + 2b * 7) 2 + 2b = 12 + 9b + (35 + 14b) Reorder the terms: 2 + 2b = 12 + 35 + 9b + 14b Combine like terms: 12 + 35 = 47 2 + 2b = 47 + 9b + 14b Combine like terms: 9b + 14b = 23b 2 + 2b = 47 + 23b Solving 2 + 2b = 47 + 23b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-23b' to each side of the equation. 2 + 2b + -23b = 47 + 23b + -23b Combine like terms: 2b + -23b = -21b 2 + -21b = 47 + 23b + -23b Combine like terms: 23b + -23b = 0 2 + -21b = 47 + 0 2 + -21b = 47 Add '-2' to each side of the equation. 2 + -2 + -21b = 47 + -2 Combine like terms: 2 + -2 = 0 0 + -21b = 47 + -2 -21b = 47 + -2 Combine like terms: 47 + -2 = 45 -21b = 45 Divide each side by '-21'. b = -2.142857143 Simplifying b = -2.142857143
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