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Simplifying 12b + -2(b + -5) = 27 + -1(b + -11) + 7b Reorder the terms: 12b + -2(-5 + b) = 27 + -1(b + -11) + 7b 12b + (-5 * -2 + b * -2) = 27 + -1(b + -11) + 7b 12b + (10 + -2b) = 27 + -1(b + -11) + 7b Reorder the terms: 10 + 12b + -2b = 27 + -1(b + -11) + 7b Combine like terms: 12b + -2b = 10b 10 + 10b = 27 + -1(b + -11) + 7b Reorder the terms: 10 + 10b = 27 + -1(-11 + b) + 7b 10 + 10b = 27 + (-11 * -1 + b * -1) + 7b 10 + 10b = 27 + (11 + -1b) + 7b Combine like terms: 27 + 11 = 38 10 + 10b = 38 + -1b + 7b Combine like terms: -1b + 7b = 6b 10 + 10b = 38 + 6b Solving 10 + 10b = 38 + 6b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6b' to each side of the equation. 10 + 10b + -6b = 38 + 6b + -6b Combine like terms: 10b + -6b = 4b 10 + 4b = 38 + 6b + -6b Combine like terms: 6b + -6b = 0 10 + 4b = 38 + 0 10 + 4b = 38 Add '-10' to each side of the equation. 10 + -10 + 4b = 38 + -10 Combine like terms: 10 + -10 = 0 0 + 4b = 38 + -10 4b = 38 + -10 Combine like terms: 38 + -10 = 28 4b = 28 Divide each side by '4'. b = 7 Simplifying b = 7
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