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Simplifying 2(3p + 1) = 8(4 + p) Reorder the terms: 2(1 + 3p) = 8(4 + p) (1 * 2 + 3p * 2) = 8(4 + p) (2 + 6p) = 8(4 + p) 2 + 6p = (4 * 8 + p * 8) 2 + 6p = (32 + 8p) Solving 2 + 6p = 32 + 8p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8p' to each side of the equation. 2 + 6p + -8p = 32 + 8p + -8p Combine like terms: 6p + -8p = -2p 2 + -2p = 32 + 8p + -8p Combine like terms: 8p + -8p = 0 2 + -2p = 32 + 0 2 + -2p = 32 Add '-2' to each side of the equation. 2 + -2 + -2p = 32 + -2 Combine like terms: 2 + -2 = 0 0 + -2p = 32 + -2 -2p = 32 + -2 Combine like terms: 32 + -2 = 30 -2p = 30 Divide each side by '-2'. p = -15 Simplifying p = -15
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