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Simplifying -3(8p + 6) + -2(6 + -23p) = 3(5 + 7p) Reorder the terms: -3(6 + 8p) + -2(6 + -23p) = 3(5 + 7p) (6 * -3 + 8p * -3) + -2(6 + -23p) = 3(5 + 7p) (-18 + -24p) + -2(6 + -23p) = 3(5 + 7p) -18 + -24p + (6 * -2 + -23p * -2) = 3(5 + 7p) -18 + -24p + (-12 + 46p) = 3(5 + 7p) Reorder the terms: -18 + -12 + -24p + 46p = 3(5 + 7p) Combine like terms: -18 + -12 = -30 -30 + -24p + 46p = 3(5 + 7p) Combine like terms: -24p + 46p = 22p -30 + 22p = 3(5 + 7p) -30 + 22p = (5 * 3 + 7p * 3) -30 + 22p = (15 + 21p) Solving -30 + 22p = 15 + 21p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-21p' to each side of the equation. -30 + 22p + -21p = 15 + 21p + -21p Combine like terms: 22p + -21p = 1p -30 + 1p = 15 + 21p + -21p Combine like terms: 21p + -21p = 0 -30 + 1p = 15 + 0 -30 + 1p = 15 Add '30' to each side of the equation. -30 + 30 + 1p = 15 + 30 Combine like terms: -30 + 30 = 0 0 + 1p = 15 + 30 1p = 15 + 30 Combine like terms: 15 + 30 = 45 1p = 45 Divide each side by '1'. p = 45 Simplifying p = 45
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