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Simplifying 5(1 + -2(2p + -1)) = -3(3p + -1) + 1 Reorder the terms: 5(1 + -2(-1 + 2p)) = -3(3p + -1) + 1 5(1 + (-1 * -2 + 2p * -2)) = -3(3p + -1) + 1 5(1 + (2 + -4p)) = -3(3p + -1) + 1 Combine like terms: 1 + 2 = 3 5(3 + -4p) = -3(3p + -1) + 1 (3 * 5 + -4p * 5) = -3(3p + -1) + 1 (15 + -20p) = -3(3p + -1) + 1 Reorder the terms: 15 + -20p = -3(-1 + 3p) + 1 15 + -20p = (-1 * -3 + 3p * -3) + 1 15 + -20p = (3 + -9p) + 1 Reorder the terms: 15 + -20p = 3 + 1 + -9p Combine like terms: 3 + 1 = 4 15 + -20p = 4 + -9p Solving 15 + -20p = 4 + -9p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '9p' to each side of the equation. 15 + -20p + 9p = 4 + -9p + 9p Combine like terms: -20p + 9p = -11p 15 + -11p = 4 + -9p + 9p Combine like terms: -9p + 9p = 0 15 + -11p = 4 + 0 15 + -11p = 4 Add '-15' to each side of the equation. 15 + -15 + -11p = 4 + -15 Combine like terms: 15 + -15 = 0 0 + -11p = 4 + -15 -11p = 4 + -15 Combine like terms: 4 + -15 = -11 -11p = -11 Divide each side by '-11'. p = 1 Simplifying p = 1
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