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Simplifying 5(p + 1) + 9 = 3(p + -2) + 6 Reorder the terms: 5(1 + p) + 9 = 3(p + -2) + 6 (1 * 5 + p * 5) + 9 = 3(p + -2) + 6 (5 + 5p) + 9 = 3(p + -2) + 6 Reorder the terms: 5 + 9 + 5p = 3(p + -2) + 6 Combine like terms: 5 + 9 = 14 14 + 5p = 3(p + -2) + 6 Reorder the terms: 14 + 5p = 3(-2 + p) + 6 14 + 5p = (-2 * 3 + p * 3) + 6 14 + 5p = (-6 + 3p) + 6 Reorder the terms: 14 + 5p = -6 + 6 + 3p Combine like terms: -6 + 6 = 0 14 + 5p = 0 + 3p 14 + 5p = 3p Solving 14 + 5p = 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. 14 + 5p + -3p = 3p + -3p Combine like terms: 5p + -3p = 2p 14 + 2p = 3p + -3p Combine like terms: 3p + -3p = 0 14 + 2p = 0 Add '-14' to each side of the equation. 14 + -14 + 2p = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 2p = 0 + -14 2p = 0 + -14 Combine like terms: 0 + -14 = -14 2p = -14 Divide each side by '2'. p = -7 Simplifying p = -7
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