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Simplifying 42 = 7(1 + -5p) + -1(6p + 6) 42 = (1 * 7 + -5p * 7) + -1(6p + 6) 42 = (7 + -35p) + -1(6p + 6) Reorder the terms: 42 = 7 + -35p + -1(6 + 6p) 42 = 7 + -35p + (6 * -1 + 6p * -1) 42 = 7 + -35p + (-6 + -6p) Reorder the terms: 42 = 7 + -6 + -35p + -6p Combine like terms: 7 + -6 = 1 42 = 1 + -35p + -6p Combine like terms: -35p + -6p = -41p 42 = 1 + -41p Solving 42 = 1 + -41p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '41p' to each side of the equation. 42 + 41p = 1 + -41p + 41p Combine like terms: -41p + 41p = 0 42 + 41p = 1 + 0 42 + 41p = 1 Add '-42' to each side of the equation. 42 + -42 + 41p = 1 + -42 Combine like terms: 42 + -42 = 0 0 + 41p = 1 + -42 41p = 1 + -42 Combine like terms: 1 + -42 = -41 41p = -41 Divide each side by '41'. p = -1 Simplifying p = -1
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