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Simplifying 33 = 2(1 + -7p) + 5(1 + 8p) 33 = (1 * 2 + -7p * 2) + 5(1 + 8p) 33 = (2 + -14p) + 5(1 + 8p) 33 = 2 + -14p + (1 * 5 + 8p * 5) 33 = 2 + -14p + (5 + 40p) Reorder the terms: 33 = 2 + 5 + -14p + 40p Combine like terms: 2 + 5 = 7 33 = 7 + -14p + 40p Combine like terms: -14p + 40p = 26p 33 = 7 + 26p Solving 33 = 7 + 26p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-26p' to each side of the equation. 33 + -26p = 7 + 26p + -26p Combine like terms: 26p + -26p = 0 33 + -26p = 7 + 0 33 + -26p = 7 Add '-33' to each side of the equation. 33 + -33 + -26p = 7 + -33 Combine like terms: 33 + -33 = 0 0 + -26p = 7 + -33 -26p = 7 + -33 Combine like terms: 7 + -33 = -26 -26p = -26 Divide each side by '-26'. p = 1 Simplifying p = 1
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