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Simplifying (2p + -3) + -1(1 + -1p) = (p + 5) + -1(2p + -3) Reorder the terms: (-3 + 2p) + -1(1 + -1p) = (p + 5) + -1(2p + -3) Remove parenthesis around (-3 + 2p) -3 + 2p + -1(1 + -1p) = (p + 5) + -1(2p + -3) -3 + 2p + (1 * -1 + -1p * -1) = (p + 5) + -1(2p + -3) -3 + 2p + (-1 + 1p) = (p + 5) + -1(2p + -3) Reorder the terms: -3 + -1 + 2p + 1p = (p + 5) + -1(2p + -3) Combine like terms: -3 + -1 = -4 -4 + 2p + 1p = (p + 5) + -1(2p + -3) Combine like terms: 2p + 1p = 3p -4 + 3p = (p + 5) + -1(2p + -3) Reorder the terms: -4 + 3p = (5 + p) + -1(2p + -3) Remove parenthesis around (5 + p) -4 + 3p = 5 + p + -1(2p + -3) Reorder the terms: -4 + 3p = 5 + p + -1(-3 + 2p) -4 + 3p = 5 + p + (-3 * -1 + 2p * -1) -4 + 3p = 5 + p + (3 + -2p) Reorder the terms: -4 + 3p = 5 + 3 + p + -2p Combine like terms: 5 + 3 = 8 -4 + 3p = 8 + p + -2p Combine like terms: p + -2p = -1p -4 + 3p = 8 + -1p Solving -4 + 3p = 8 + -1p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add 'p' to each side of the equation. -4 + 3p + p = 8 + -1p + p Combine like terms: 3p + p = 4p -4 + 4p = 8 + -1p + p Combine like terms: -1p + p = 0 -4 + 4p = 8 + 0 -4 + 4p = 8 Add '4' to each side of the equation. -4 + 4 + 4p = 8 + 4 Combine like terms: -4 + 4 = 0 0 + 4p = 8 + 4 4p = 8 + 4 Combine like terms: 8 + 4 = 12 4p = 12 Divide each side by '4'. p = 3 Simplifying p = 3
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