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Simplifying 5(p + 3) + 9 = (p + -2) * 3 + 6 Reorder the terms: 5(3 + p) + 9 = (p + -2) * 3 + 6 (3 * 5 + p * 5) + 9 = (p + -2) * 3 + 6 (15 + 5p) + 9 = (p + -2) * 3 + 6 Reorder the terms: 15 + 9 + 5p = (p + -2) * 3 + 6 Combine like terms: 15 + 9 = 24 24 + 5p = (p + -2) * 3 + 6 Reorder the terms: 24 + 5p = (-2 + p) * 3 + 6 Reorder the terms for easier multiplication: 24 + 5p = 3(-2 + p) + 6 24 + 5p = (-2 * 3 + p * 3) + 6 24 + 5p = (-6 + 3p) + 6 Reorder the terms: 24 + 5p = -6 + 6 + 3p Combine like terms: -6 + 6 = 0 24 + 5p = 0 + 3p 24 + 5p = 3p Solving 24 + 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. 24 + 5p + -3p = 3p + -3p Combine like terms: 5p + -3p = 2p 24 + 2p = 3p + -3p Combine like terms: 3p + -3p = 0 24 + 2p = 0 Add '-24' to each side of the equation. 24 + -24 + 2p = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 2p = 0 + -24 2p = 0 + -24 Combine like terms: 0 + -24 = -24 2p = -24 Divide each side by '2'. p = -12 Simplifying p = -12
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