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Simplifying -100p + 90(1 + -1p) = 80p + -70(1 + -1p) -100p + (1 * 90 + -1p * 90) = 80p + -70(1 + -1p) -100p + (90 + -90p) = 80p + -70(1 + -1p) Reorder the terms: 90 + -100p + -90p = 80p + -70(1 + -1p) Combine like terms: -100p + -90p = -190p 90 + -190p = 80p + -70(1 + -1p) 90 + -190p = 80p + (1 * -70 + -1p * -70) 90 + -190p = 80p + (-70 + 70p) Reorder the terms: 90 + -190p = -70 + 80p + 70p Combine like terms: 80p + 70p = 150p 90 + -190p = -70 + 150p Solving 90 + -190p = -70 + 150p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-150p' to each side of the equation. 90 + -190p + -150p = -70 + 150p + -150p Combine like terms: -190p + -150p = -340p 90 + -340p = -70 + 150p + -150p Combine like terms: 150p + -150p = 0 90 + -340p = -70 + 0 90 + -340p = -70 Add '-90' to each side of the equation. 90 + -90 + -340p = -70 + -90 Combine like terms: 90 + -90 = 0 0 + -340p = -70 + -90 -340p = -70 + -90 Combine like terms: -70 + -90 = -160 -340p = -160 Divide each side by '-340'. p = 0.4705882353 Simplifying p = 0.4705882353
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