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Simplifying 55 = 3(1 + 4b) + 8(1 + 4b) 55 = (1 * 3 + 4b * 3) + 8(1 + 4b) 55 = (3 + 12b) + 8(1 + 4b) 55 = 3 + 12b + (1 * 8 + 4b * 8) 55 = 3 + 12b + (8 + 32b) Reorder the terms: 55 = 3 + 8 + 12b + 32b Combine like terms: 3 + 8 = 11 55 = 11 + 12b + 32b Combine like terms: 12b + 32b = 44b 55 = 11 + 44b Solving 55 = 11 + 44b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-44b' to each side of the equation. 55 + -44b = 11 + 44b + -44b Combine like terms: 44b + -44b = 0 55 + -44b = 11 + 0 55 + -44b = 11 Add '-55' to each side of the equation. 55 + -55 + -44b = 11 + -55 Combine like terms: 55 + -55 = 0 0 + -44b = 11 + -55 -44b = 11 + -55 Combine like terms: 11 + -55 = -44 -44b = -44 Divide each side by '-44'. b = 1 Simplifying b = 1
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