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Simplifying 12b + 5(-2b + -3) + 5 = -3(4b + 1) + 2(3b + -1) + -1 Reorder the terms: 12b + 5(-3 + -2b) + 5 = -3(4b + 1) + 2(3b + -1) + -1 12b + (-3 * 5 + -2b * 5) + 5 = -3(4b + 1) + 2(3b + -1) + -1 12b + (-15 + -10b) + 5 = -3(4b + 1) + 2(3b + -1) + -1 Reorder the terms: -15 + 5 + 12b + -10b = -3(4b + 1) + 2(3b + -1) + -1 Combine like terms: -15 + 5 = -10 -10 + 12b + -10b = -3(4b + 1) + 2(3b + -1) + -1 Combine like terms: 12b + -10b = 2b -10 + 2b = -3(4b + 1) + 2(3b + -1) + -1 Reorder the terms: -10 + 2b = -3(1 + 4b) + 2(3b + -1) + -1 -10 + 2b = (1 * -3 + 4b * -3) + 2(3b + -1) + -1 -10 + 2b = (-3 + -12b) + 2(3b + -1) + -1 Reorder the terms: -10 + 2b = -3 + -12b + 2(-1 + 3b) + -1 -10 + 2b = -3 + -12b + (-1 * 2 + 3b * 2) + -1 -10 + 2b = -3 + -12b + (-2 + 6b) + -1 Reorder the terms: -10 + 2b = -3 + -2 + -1 + -12b + 6b Combine like terms: -3 + -2 = -5 -10 + 2b = -5 + -1 + -12b + 6b Combine like terms: -5 + -1 = -6 -10 + 2b = -6 + -12b + 6b Combine like terms: -12b + 6b = -6b -10 + 2b = -6 + -6b Solving -10 + 2b = -6 + -6b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6b' to each side of the equation. -10 + 2b + 6b = -6 + -6b + 6b Combine like terms: 2b + 6b = 8b -10 + 8b = -6 + -6b + 6b Combine like terms: -6b + 6b = 0 -10 + 8b = -6 + 0 -10 + 8b = -6 Add '10' to each side of the equation. -10 + 10 + 8b = -6 + 10 Combine like terms: -10 + 10 = 0 0 + 8b = -6 + 10 8b = -6 + 10 Combine like terms: -6 + 10 = 4 8b = 4 Divide each side by '8'. b = 0.5 Simplifying b = 0.5
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