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Simplifying 5(1 + 6b) = 8(b + -4) + -7 (1 * 5 + 6b * 5) = 8(b + -4) + -7 (5 + 30b) = 8(b + -4) + -7 Reorder the terms: 5 + 30b = 8(-4 + b) + -7 5 + 30b = (-4 * 8 + b * 8) + -7 5 + 30b = (-32 + 8b) + -7 Reorder the terms: 5 + 30b = -32 + -7 + 8b Combine like terms: -32 + -7 = -39 5 + 30b = -39 + 8b Solving 5 + 30b = -39 + 8b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8b' to each side of the equation. 5 + 30b + -8b = -39 + 8b + -8b Combine like terms: 30b + -8b = 22b 5 + 22b = -39 + 8b + -8b Combine like terms: 8b + -8b = 0 5 + 22b = -39 + 0 5 + 22b = -39 Add '-5' to each side of the equation. 5 + -5 + 22b = -39 + -5 Combine like terms: 5 + -5 = 0 0 + 22b = -39 + -5 22b = -39 + -5 Combine like terms: -39 + -5 = -44 22b = -44 Divide each side by '22'. b = -2 Simplifying b = -2
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