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Simplifying 3 + -1(8p + 6) + -2(1 + -23p) = 3(5 + 7p) Reorder the terms: 3 + -1(6 + 8p) + -2(1 + -23p) = 3(5 + 7p) 3 + (6 * -1 + 8p * -1) + -2(1 + -23p) = 3(5 + 7p) 3 + (-6 + -8p) + -2(1 + -23p) = 3(5 + 7p) 3 + -6 + -8p + (1 * -2 + -23p * -2) = 3(5 + 7p) 3 + -6 + -8p + (-2 + 46p) = 3(5 + 7p) Reorder the terms: 3 + -6 + -2 + -8p + 46p = 3(5 + 7p) Combine like terms: 3 + -6 = -3 -3 + -2 + -8p + 46p = 3(5 + 7p) Combine like terms: -3 + -2 = -5 -5 + -8p + 46p = 3(5 + 7p) Combine like terms: -8p + 46p = 38p -5 + 38p = 3(5 + 7p) -5 + 38p = (5 * 3 + 7p * 3) -5 + 38p = (15 + 21p) Solving -5 + 38p = 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. -5 + 38p + -21p = 15 + 21p + -21p Combine like terms: 38p + -21p = 17p -5 + 17p = 15 + 21p + -21p Combine like terms: 21p + -21p = 0 -5 + 17p = 15 + 0 -5 + 17p = 15 Add '5' to each side of the equation. -5 + 5 + 17p = 15 + 5 Combine like terms: -5 + 5 = 0 0 + 17p = 15 + 5 17p = 15 + 5 Combine like terms: 15 + 5 = 20 17p = 20 Divide each side by '17'. p = 1.176470588 Simplifying p = 1.176470588
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