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Simplifying 3(p + 7) + -1(4p + -1) = 5(2p + -30) + 1 Reorder the terms: 3(7 + p) + -1(4p + -1) = 5(2p + -30) + 1 (7 * 3 + p * 3) + -1(4p + -1) = 5(2p + -30) + 1 (21 + 3p) + -1(4p + -1) = 5(2p + -30) + 1 Reorder the terms: 21 + 3p + -1(-1 + 4p) = 5(2p + -30) + 1 21 + 3p + (-1 * -1 + 4p * -1) = 5(2p + -30) + 1 21 + 3p + (1 + -4p) = 5(2p + -30) + 1 Reorder the terms: 21 + 1 + 3p + -4p = 5(2p + -30) + 1 Combine like terms: 21 + 1 = 22 22 + 3p + -4p = 5(2p + -30) + 1 Combine like terms: 3p + -4p = -1p 22 + -1p = 5(2p + -30) + 1 Reorder the terms: 22 + -1p = 5(-30 + 2p) + 1 22 + -1p = (-30 * 5 + 2p * 5) + 1 22 + -1p = (-150 + 10p) + 1 Reorder the terms: 22 + -1p = -150 + 1 + 10p Combine like terms: -150 + 1 = -149 22 + -1p = -149 + 10p Solving 22 + -1p = -149 + 10p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10p' to each side of the equation. 22 + -1p + -10p = -149 + 10p + -10p Combine like terms: -1p + -10p = -11p 22 + -11p = -149 + 10p + -10p Combine like terms: 10p + -10p = 0 22 + -11p = -149 + 0 22 + -11p = -149 Add '-22' to each side of the equation. 22 + -22 + -11p = -149 + -22 Combine like terms: 22 + -22 = 0 0 + -11p = -149 + -22 -11p = -149 + -22 Combine like terms: -149 + -22 = -171 -11p = -171 Divide each side by '-11'. p = 15.54545455 Simplifying p = 15.54545455
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