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Simplifying 5(3b + 7) + 2(5b + 8c) + -3c + -1b = 0 Reorder the terms: 5(7 + 3b) + 2(5b + 8c) + -3c + -1b = 0 (7 * 5 + 3b * 5) + 2(5b + 8c) + -3c + -1b = 0 (35 + 15b) + 2(5b + 8c) + -3c + -1b = 0 35 + 15b + (5b * 2 + 8c * 2) + -3c + -1b = 0 35 + 15b + (10b + 16c) + -3c + -1b = 0 Reorder the terms: 35 + 15b + 10b + -1b + 16c + -3c = 0 Combine like terms: 15b + 10b = 25b 35 + 25b + -1b + 16c + -3c = 0 Combine like terms: 25b + -1b = 24b 35 + 24b + 16c + -3c = 0 Combine like terms: 16c + -3c = 13c 35 + 24b + 13c = 0 Solving 35 + 24b + 13c = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + 24b + -35 + 13c = 0 + -35 Reorder the terms: 35 + -35 + 24b + 13c = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 24b + 13c = 0 + -35 24b + 13c = 0 + -35 Combine like terms: 0 + -35 = -35 24b + 13c = -35 Add '-13c' to each side of the equation. 24b + 13c + -13c = -35 + -13c Combine like terms: 13c + -13c = 0 24b + 0 = -35 + -13c 24b = -35 + -13c Divide each side by '24'. b = -1.458333333 + -0.5416666667c Simplifying b = -1.458333333 + -0.5416666667c
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