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Simplifying p + -1(9 + -1p) + 4(p + 2) = 12 + 3(p + 2) + 2 p + (9 * -1 + -1p * -1) + 4(p + 2) = 12 + 3(p + 2) + 2 p + (-9 + 1p) + 4(p + 2) = 12 + 3(p + 2) + 2 Reorder the terms: p + -9 + 1p + 4(2 + p) = 12 + 3(p + 2) + 2 p + -9 + 1p + (2 * 4 + p * 4) = 12 + 3(p + 2) + 2 p + -9 + 1p + (8 + 4p) = 12 + 3(p + 2) + 2 Reorder the terms: -9 + 8 + p + 1p + 4p = 12 + 3(p + 2) + 2 Combine like terms: -9 + 8 = -1 -1 + p + 1p + 4p = 12 + 3(p + 2) + 2 Combine like terms: p + 1p = 2p -1 + 2p + 4p = 12 + 3(p + 2) + 2 Combine like terms: 2p + 4p = 6p -1 + 6p = 12 + 3(p + 2) + 2 Reorder the terms: -1 + 6p = 12 + 3(2 + p) + 2 -1 + 6p = 12 + (2 * 3 + p * 3) + 2 -1 + 6p = 12 + (6 + 3p) + 2 Reorder the terms: -1 + 6p = 12 + 6 + 2 + 3p Combine like terms: 12 + 6 = 18 -1 + 6p = 18 + 2 + 3p Combine like terms: 18 + 2 = 20 -1 + 6p = 20 + 3p Solving -1 + 6p = 20 + 3p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3p' to each side of the equation. -1 + 6p + -3p = 20 + 3p + -3p Combine like terms: 6p + -3p = 3p -1 + 3p = 20 + 3p + -3p Combine like terms: 3p + -3p = 0 -1 + 3p = 20 + 0 -1 + 3p = 20 Add '1' to each side of the equation. -1 + 1 + 3p = 20 + 1 Combine like terms: -1 + 1 = 0 0 + 3p = 20 + 1 3p = 20 + 1 Combine like terms: 20 + 1 = 21 3p = 21 Divide each side by '3'. p = 7 Simplifying p = 7
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