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Simplifying 5(b + c) = 7(b + -1c) (b * 5 + c * 5) = 7(b + -1c) (5b + 5c) = 7(b + -1c) 5b + 5c = (b * 7 + -1c * 7) 5b + 5c = (7b + -7c) Solving 5b + 5c = 7b + -7c 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. 5b + -7b + 5c = 7b + -7b + -7c Combine like terms: 5b + -7b = -2b -2b + 5c = 7b + -7b + -7c Combine like terms: 7b + -7b = 0 -2b + 5c = 0 + -7c -2b + 5c = -7c Add '-5c' to each side of the equation. -2b + 5c + -5c = -7c + -5c Combine like terms: 5c + -5c = 0 -2b + 0 = -7c + -5c -2b = -7c + -5c Combine like terms: -7c + -5c = -12c -2b = -12c Divide each side by '-2'. b = 6c Simplifying b = 6c
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