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Simplifying 2(b + -5) + 3(b + -2) = 8 + 7(b + 4) Reorder the terms: 2(-5 + b) + 3(b + -2) = 8 + 7(b + 4) (-5 * 2 + b * 2) + 3(b + -2) = 8 + 7(b + 4) (-10 + 2b) + 3(b + -2) = 8 + 7(b + 4) Reorder the terms: -10 + 2b + 3(-2 + b) = 8 + 7(b + 4) -10 + 2b + (-2 * 3 + b * 3) = 8 + 7(b + 4) -10 + 2b + (-6 + 3b) = 8 + 7(b + 4) Reorder the terms: -10 + -6 + 2b + 3b = 8 + 7(b + 4) Combine like terms: -10 + -6 = -16 -16 + 2b + 3b = 8 + 7(b + 4) Combine like terms: 2b + 3b = 5b -16 + 5b = 8 + 7(b + 4) Reorder the terms: -16 + 5b = 8 + 7(4 + b) -16 + 5b = 8 + (4 * 7 + b * 7) -16 + 5b = 8 + (28 + 7b) Combine like terms: 8 + 28 = 36 -16 + 5b = 36 + 7b Solving -16 + 5b = 36 + 7b 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. -16 + 5b + -7b = 36 + 7b + -7b Combine like terms: 5b + -7b = -2b -16 + -2b = 36 + 7b + -7b Combine like terms: 7b + -7b = 0 -16 + -2b = 36 + 0 -16 + -2b = 36 Add '16' to each side of the equation. -16 + 16 + -2b = 36 + 16 Combine like terms: -16 + 16 = 0 0 + -2b = 36 + 16 -2b = 36 + 16 Combine like terms: 36 + 16 = 52 -2b = 52 Divide each side by '-2'. b = -26 Simplifying b = -26
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