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Simplifying 2(p + 5) + 7 = 8(5 + -1p) + -2(-7 + -3p) + 4 Reorder the terms: 2(5 + p) + 7 = 8(5 + -1p) + -2(-7 + -3p) + 4 (5 * 2 + p * 2) + 7 = 8(5 + -1p) + -2(-7 + -3p) + 4 (10 + 2p) + 7 = 8(5 + -1p) + -2(-7 + -3p) + 4 Reorder the terms: 10 + 7 + 2p = 8(5 + -1p) + -2(-7 + -3p) + 4 Combine like terms: 10 + 7 = 17 17 + 2p = 8(5 + -1p) + -2(-7 + -3p) + 4 17 + 2p = (5 * 8 + -1p * 8) + -2(-7 + -3p) + 4 17 + 2p = (40 + -8p) + -2(-7 + -3p) + 4 17 + 2p = 40 + -8p + (-7 * -2 + -3p * -2) + 4 17 + 2p = 40 + -8p + (14 + 6p) + 4 Reorder the terms: 17 + 2p = 40 + 14 + 4 + -8p + 6p Combine like terms: 40 + 14 = 54 17 + 2p = 54 + 4 + -8p + 6p Combine like terms: 54 + 4 = 58 17 + 2p = 58 + -8p + 6p Combine like terms: -8p + 6p = -2p 17 + 2p = 58 + -2p Solving 17 + 2p = 58 + -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. 17 + 2p + 2p = 58 + -2p + 2p Combine like terms: 2p + 2p = 4p 17 + 4p = 58 + -2p + 2p Combine like terms: -2p + 2p = 0 17 + 4p = 58 + 0 17 + 4p = 58 Add '-17' to each side of the equation. 17 + -17 + 4p = 58 + -17 Combine like terms: 17 + -17 = 0 0 + 4p = 58 + -17 4p = 58 + -17 Combine like terms: 58 + -17 = 41 4p = 41 Divide each side by '4'. p = 10.25 Simplifying p = 10.25
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