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Simplifying 8p + -31 = 1 + 8(7p + 8) Reorder the terms: -31 + 8p = 1 + 8(7p + 8) Reorder the terms: -31 + 8p = 1 + 8(8 + 7p) -31 + 8p = 1 + (8 * 8 + 7p * 8) -31 + 8p = 1 + (64 + 56p) Combine like terms: 1 + 64 = 65 -31 + 8p = 65 + 56p Solving -31 + 8p = 65 + 56p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-56p' to each side of the equation. -31 + 8p + -56p = 65 + 56p + -56p Combine like terms: 8p + -56p = -48p -31 + -48p = 65 + 56p + -56p Combine like terms: 56p + -56p = 0 -31 + -48p = 65 + 0 -31 + -48p = 65 Add '31' to each side of the equation. -31 + 31 + -48p = 65 + 31 Combine like terms: -31 + 31 = 0 0 + -48p = 65 + 31 -48p = 65 + 31 Combine like terms: 65 + 31 = 96 -48p = 96 Divide each side by '-48'. p = -2 Simplifying p = -2
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