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Simplifying -3(5b + -9) + 3(7b + 4) = -1b + 8(b + 2) Reorder the terms: -3(-9 + 5b) + 3(7b + 4) = -1b + 8(b + 2) (-9 * -3 + 5b * -3) + 3(7b + 4) = -1b + 8(b + 2) (27 + -15b) + 3(7b + 4) = -1b + 8(b + 2) Reorder the terms: 27 + -15b + 3(4 + 7b) = -1b + 8(b + 2) 27 + -15b + (4 * 3 + 7b * 3) = -1b + 8(b + 2) 27 + -15b + (12 + 21b) = -1b + 8(b + 2) Reorder the terms: 27 + 12 + -15b + 21b = -1b + 8(b + 2) Combine like terms: 27 + 12 = 39 39 + -15b + 21b = -1b + 8(b + 2) Combine like terms: -15b + 21b = 6b 39 + 6b = -1b + 8(b + 2) Reorder the terms: 39 + 6b = -1b + 8(2 + b) 39 + 6b = -1b + (2 * 8 + b * 8) 39 + 6b = -1b + (16 + 8b) Reorder the terms: 39 + 6b = 16 + -1b + 8b Combine like terms: -1b + 8b = 7b 39 + 6b = 16 + 7b Solving 39 + 6b = 16 + 7b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7b' to each side of the equation. 39 + 6b + -7b = 16 + 7b + -7b Combine like terms: 6b + -7b = -1b 39 + -1b = 16 + 7b + -7b Combine like terms: 7b + -7b = 0 39 + -1b = 16 + 0 39 + -1b = 16 Add '-39' to each side of the equation. 39 + -39 + -1b = 16 + -39 Combine like terms: 39 + -39 = 0 0 + -1b = 16 + -39 -1b = 16 + -39 Combine like terms: 16 + -39 = -23 -1b = -23 Divide each side by '-1'. b = 23 Simplifying b = 23
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