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Simplifying 0.5(p + 6) = 3.1(3 + -1p) Reorder the terms: 0.5(6 + p) = 3.1(3 + -1p) (6 * 0.5 + p * 0.5) = 3.1(3 + -1p) (3 + 0.5p) = 3.1(3 + -1p) 3 + 0.5p = (3 * 3.1 + -1p * 3.1) 3 + 0.5p = (9.3 + -3.1p) Solving 3 + 0.5p = 9.3 + -3.1p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3.1p' to each side of the equation. 3 + 0.5p + 3.1p = 9.3 + -3.1p + 3.1p Combine like terms: 0.5p + 3.1p = 3.6p 3 + 3.6p = 9.3 + -3.1p + 3.1p Combine like terms: -3.1p + 3.1p = 0.0 3 + 3.6p = 9.3 + 0.0 3 + 3.6p = 9.3 Add '-3' to each side of the equation. 3 + -3 + 3.6p = 9.3 + -3 Combine like terms: 3 + -3 = 0 0 + 3.6p = 9.3 + -3 3.6p = 9.3 + -3 Combine like terms: 9.3 + -3 = 6.3 3.6p = 6.3 Divide each side by '3.6'. p = 1.75 Simplifying p = 1.75
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