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Simplifying 0.5(b + -3) + -1(0.5 + b) = b + 3 Reorder the terms: 0.5(-3 + b) + -1(0.5 + b) = b + 3 (-3 * 0.5 + b * 0.5) + -1(0.5 + b) = b + 3 (-1.5 + 0.5b) + -1(0.5 + b) = b + 3 -1.5 + 0.5b + (0.5 * -1 + b * -1) = b + 3 -1.5 + 0.5b + (-0.5 + -1b) = b + 3 Reorder the terms: -1.5 + -0.5 + 0.5b + -1b = b + 3 Combine like terms: -1.5 + -0.5 = -2 -2 + 0.5b + -1b = b + 3 Combine like terms: 0.5b + -1b = -0.5b -2 + -0.5b = b + 3 Reorder the terms: -2 + -0.5b = 3 + b Solving -2 + -0.5b = 3 + b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1b' to each side of the equation. -2 + -0.5b + -1b = 3 + b + -1b Combine like terms: -0.5b + -1b = -1.5b -2 + -1.5b = 3 + b + -1b Combine like terms: b + -1b = 0 -2 + -1.5b = 3 + 0 -2 + -1.5b = 3 Add '2' to each side of the equation. -2 + 2 + -1.5b = 3 + 2 Combine like terms: -2 + 2 = 0 0 + -1.5b = 3 + 2 -1.5b = 3 + 2 Combine like terms: 3 + 2 = 5 -1.5b = 5 Divide each side by '-1.5'. b = -3.333333333 Simplifying b = -3.333333333
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