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Simplifying 3(b + -5) + 6(2b + -1) = 7(2b + 1) Reorder the terms: 3(-5 + b) + 6(2b + -1) = 7(2b + 1) (-5 * 3 + b * 3) + 6(2b + -1) = 7(2b + 1) (-15 + 3b) + 6(2b + -1) = 7(2b + 1) Reorder the terms: -15 + 3b + 6(-1 + 2b) = 7(2b + 1) -15 + 3b + (-1 * 6 + 2b * 6) = 7(2b + 1) -15 + 3b + (-6 + 12b) = 7(2b + 1) Reorder the terms: -15 + -6 + 3b + 12b = 7(2b + 1) Combine like terms: -15 + -6 = -21 -21 + 3b + 12b = 7(2b + 1) Combine like terms: 3b + 12b = 15b -21 + 15b = 7(2b + 1) Reorder the terms: -21 + 15b = 7(1 + 2b) -21 + 15b = (1 * 7 + 2b * 7) -21 + 15b = (7 + 14b) Solving -21 + 15b = 7 + 14b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-14b' to each side of the equation. -21 + 15b + -14b = 7 + 14b + -14b Combine like terms: 15b + -14b = 1b -21 + 1b = 7 + 14b + -14b Combine like terms: 14b + -14b = 0 -21 + 1b = 7 + 0 -21 + 1b = 7 Add '21' to each side of the equation. -21 + 21 + 1b = 7 + 21 Combine like terms: -21 + 21 = 0 0 + 1b = 7 + 21 1b = 7 + 21 Combine like terms: 7 + 21 = 28 1b = 28 Divide each side by '1'. b = 28 Simplifying b = 28
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