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Simplifying p(0.58) + (0.95)(1 + -1p) = (0.93) * p + (0.7)(1 + -1p) Reorder the terms for easier multiplication: 0.58p + (0.95)(1 + -1p) = (0.93) * p + (0.7)(1 + -1p) 0.58p + (1 * 0.95 + -1p * 0.95) = (0.93) * p + (0.7)(1 + -1p) 0.58p + (0.95 + -0.95p) = (0.93) * p + (0.7)(1 + -1p) Reorder the terms: 0.95 + 0.58p + -0.95p = (0.93) * p + (0.7)(1 + -1p) Combine like terms: 0.58p + -0.95p = -0.37p 0.95 + -0.37p = (0.93) * p + (0.7)(1 + -1p) 0.95 + -0.37p = 0.93p + (1 * 0.7 + -1p * 0.7) 0.95 + -0.37p = 0.93p + (0.7 + -0.7p) Reorder the terms: 0.95 + -0.37p = 0.7 + 0.93p + -0.7p Combine like terms: 0.93p + -0.7p = 0.23p 0.95 + -0.37p = 0.7 + 0.23p Solving 0.95 + -0.37p = 0.7 + 0.23p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.23p' to each side of the equation. 0.95 + -0.37p + -0.23p = 0.7 + 0.23p + -0.23p Combine like terms: -0.37p + -0.23p = -0.6p 0.95 + -0.6p = 0.7 + 0.23p + -0.23p Combine like terms: 0.23p + -0.23p = 0.00 0.95 + -0.6p = 0.7 + 0.00 0.95 + -0.6p = 0.7 Add '-0.95' to each side of the equation. 0.95 + -0.95 + -0.6p = 0.7 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + -0.6p = 0.7 + -0.95 -0.6p = 0.7 + -0.95 Combine like terms: 0.7 + -0.95 = -0.25 -0.6p = -0.25 Divide each side by '-0.6'. p = 0.4166666667 Simplifying p = 0.4166666667
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