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