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Simplifying 38 = 5(3b + -6) + 7(-1b + 4) Reorder the terms: 38 = 5(-6 + 3b) + 7(-1b + 4) 38 = (-6 * 5 + 3b * 5) + 7(-1b + 4) 38 = (-30 + 15b) + 7(-1b + 4) Reorder the terms: 38 = -30 + 15b + 7(4 + -1b) 38 = -30 + 15b + (4 * 7 + -1b * 7) 38 = -30 + 15b + (28 + -7b) Reorder the terms: 38 = -30 + 28 + 15b + -7b Combine like terms: -30 + 28 = -2 38 = -2 + 15b + -7b Combine like terms: 15b + -7b = 8b 38 = -2 + 8b Solving 38 = -2 + 8b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8b' to each side of the equation. 38 + -8b = -2 + 8b + -8b Combine like terms: 8b + -8b = 0 38 + -8b = -2 + 0 38 + -8b = -2 Add '-38' to each side of the equation. 38 + -38 + -8b = -2 + -38 Combine like terms: 38 + -38 = 0 0 + -8b = -2 + -38 -8b = -2 + -38 Combine like terms: -2 + -38 = -40 -8b = -40 Divide each side by '-8'. b = 5 Simplifying b = 5
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