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Simplifying 31 = -1(1 + 6p) + 4(p + 6) 31 = (1 * -1 + 6p * -1) + 4(p + 6) 31 = (-1 + -6p) + 4(p + 6) Reorder the terms: 31 = -1 + -6p + 4(6 + p) 31 = -1 + -6p + (6 * 4 + p * 4) 31 = -1 + -6p + (24 + 4p) Reorder the terms: 31 = -1 + 24 + -6p + 4p Combine like terms: -1 + 24 = 23 31 = 23 + -6p + 4p Combine like terms: -6p + 4p = -2p 31 = 23 + -2p Solving 31 = 23 + -2p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2p' to each side of the equation. 31 + 2p = 23 + -2p + 2p Combine like terms: -2p + 2p = 0 31 + 2p = 23 + 0 31 + 2p = 23 Add '-31' to each side of the equation. 31 + -31 + 2p = 23 + -31 Combine like terms: 31 + -31 = 0 0 + 2p = 23 + -31 2p = 23 + -31 Combine like terms: 23 + -31 = -8 2p = -8 Divide each side by '2'. p = -4 Simplifying p = -4
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