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Simplifying 4(b + -7) + -1(b + 5) = 2(1 + -1b) Reorder the terms: 4(-7 + b) + -1(b + 5) = 2(1 + -1b) (-7 * 4 + b * 4) + -1(b + 5) = 2(1 + -1b) (-28 + 4b) + -1(b + 5) = 2(1 + -1b) Reorder the terms: -28 + 4b + -1(5 + b) = 2(1 + -1b) -28 + 4b + (5 * -1 + b * -1) = 2(1 + -1b) -28 + 4b + (-5 + -1b) = 2(1 + -1b) Reorder the terms: -28 + -5 + 4b + -1b = 2(1 + -1b) Combine like terms: -28 + -5 = -33 -33 + 4b + -1b = 2(1 + -1b) Combine like terms: 4b + -1b = 3b -33 + 3b = 2(1 + -1b) -33 + 3b = (1 * 2 + -1b * 2) -33 + 3b = (2 + -2b) Solving -33 + 3b = 2 + -2b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2b' to each side of the equation. -33 + 3b + 2b = 2 + -2b + 2b Combine like terms: 3b + 2b = 5b -33 + 5b = 2 + -2b + 2b Combine like terms: -2b + 2b = 0 -33 + 5b = 2 + 0 -33 + 5b = 2 Add '33' to each side of the equation. -33 + 33 + 5b = 2 + 33 Combine like terms: -33 + 33 = 0 0 + 5b = 2 + 33 5b = 2 + 33 Combine like terms: 2 + 33 = 35 5b = 35 Divide each side by '5'. b = 7 Simplifying b = 7
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