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Simplifying -7(1 + 2b) + -6(3 + -5b) = (4 + 3b) + -45 (1 * -7 + 2b * -7) + -6(3 + -5b) = (4 + 3b) + -45 (-7 + -14b) + -6(3 + -5b) = (4 + 3b) + -45 -7 + -14b + (3 * -6 + -5b * -6) = (4 + 3b) + -45 -7 + -14b + (-18 + 30b) = (4 + 3b) + -45 Reorder the terms: -7 + -18 + -14b + 30b = (4 + 3b) + -45 Combine like terms: -7 + -18 = -25 -25 + -14b + 30b = (4 + 3b) + -45 Combine like terms: -14b + 30b = 16b -25 + 16b = (4 + 3b) + -45 Remove parenthesis around (4 + 3b) -25 + 16b = 4 + 3b + -45 Reorder the terms: -25 + 16b = 4 + -45 + 3b Combine like terms: 4 + -45 = -41 -25 + 16b = -41 + 3b Solving -25 + 16b = -41 + 3b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3b' to each side of the equation. -25 + 16b + -3b = -41 + 3b + -3b Combine like terms: 16b + -3b = 13b -25 + 13b = -41 + 3b + -3b Combine like terms: 3b + -3b = 0 -25 + 13b = -41 + 0 -25 + 13b = -41 Add '25' to each side of the equation. -25 + 25 + 13b = -41 + 25 Combine like terms: -25 + 25 = 0 0 + 13b = -41 + 25 13b = -41 + 25 Combine like terms: -41 + 25 = -16 13b = -16 Divide each side by '13'. b = -1.230769231 Simplifying b = -1.230769231
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