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Simplifying 2(p + -2) + 3 = 12 + -1(p + 1) Reorder the terms: 2(-2 + p) + 3 = 12 + -1(p + 1) (-2 * 2 + p * 2) + 3 = 12 + -1(p + 1) (-4 + 2p) + 3 = 12 + -1(p + 1) Reorder the terms: -4 + 3 + 2p = 12 + -1(p + 1) Combine like terms: -4 + 3 = -1 -1 + 2p = 12 + -1(p + 1) Reorder the terms: -1 + 2p = 12 + -1(1 + p) -1 + 2p = 12 + (1 * -1 + p * -1) -1 + 2p = 12 + (-1 + -1p) Combine like terms: 12 + -1 = 11 -1 + 2p = 11 + -1p Solving -1 + 2p = 11 + -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. -1 + 2p + p = 11 + -1p + p Combine like terms: 2p + p = 3p -1 + 3p = 11 + -1p + p Combine like terms: -1p + p = 0 -1 + 3p = 11 + 0 -1 + 3p = 11 Add '1' to each side of the equation. -1 + 1 + 3p = 11 + 1 Combine like terms: -1 + 1 = 0 0 + 3p = 11 + 1 3p = 11 + 1 Combine like terms: 11 + 1 = 12 3p = 12 Divide each side by '3'. p = 4 Simplifying p = 4
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