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Simplifying 3(6 + -5p) + (12 + p) = 2(5 + -2p) (6 * 3 + -5p * 3) + (12 + p) = 2(5 + -2p) (18 + -15p) + (12 + p) = 2(5 + -2p) Remove parenthesis around (12 + p) 18 + -15p + 12 + p = 2(5 + -2p) Reorder the terms: 18 + 12 + -15p + p = 2(5 + -2p) Combine like terms: 18 + 12 = 30 30 + -15p + p = 2(5 + -2p) Combine like terms: -15p + p = -14p 30 + -14p = 2(5 + -2p) 30 + -14p = (5 * 2 + -2p * 2) 30 + -14p = (10 + -4p) Solving 30 + -14p = 10 + -4p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4p' to each side of the equation. 30 + -14p + 4p = 10 + -4p + 4p Combine like terms: -14p + 4p = -10p 30 + -10p = 10 + -4p + 4p Combine like terms: -4p + 4p = 0 30 + -10p = 10 + 0 30 + -10p = 10 Add '-30' to each side of the equation. 30 + -30 + -10p = 10 + -30 Combine like terms: 30 + -30 = 0 0 + -10p = 10 + -30 -10p = 10 + -30 Combine like terms: 10 + -30 = -20 -10p = -20 Divide each side by '-10'. p = 2 Simplifying p = 2
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