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Simplifying 20p + (-20)(1 + -1p) = 15p + 30(1 + -1p) 20p + (1 * -20 + -1p * -20) = 15p + 30(1 + -1p) 20p + (-20 + 20p) = 15p + 30(1 + -1p) Reorder the terms: -20 + 20p + 20p = 15p + 30(1 + -1p) Combine like terms: 20p + 20p = 40p -20 + 40p = 15p + 30(1 + -1p) -20 + 40p = 15p + (1 * 30 + -1p * 30) -20 + 40p = 15p + (30 + -30p) Reorder the terms: -20 + 40p = 30 + 15p + -30p Combine like terms: 15p + -30p = -15p -20 + 40p = 30 + -15p Solving -20 + 40p = 30 + -15p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '15p' to each side of the equation. -20 + 40p + 15p = 30 + -15p + 15p Combine like terms: 40p + 15p = 55p -20 + 55p = 30 + -15p + 15p Combine like terms: -15p + 15p = 0 -20 + 55p = 30 + 0 -20 + 55p = 30 Add '20' to each side of the equation. -20 + 20 + 55p = 30 + 20 Combine like terms: -20 + 20 = 0 0 + 55p = 30 + 20 55p = 30 + 20 Combine like terms: 30 + 20 = 50 55p = 50 Divide each side by '55'. p = 0.9090909091 Simplifying p = 0.9090909091
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