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Simplifying 4(2p + -5) + 5(p + -4) + -2(p + 9) = 30 Reorder the terms: 4(-5 + 2p) + 5(p + -4) + -2(p + 9) = 30 (-5 * 4 + 2p * 4) + 5(p + -4) + -2(p + 9) = 30 (-20 + 8p) + 5(p + -4) + -2(p + 9) = 30 Reorder the terms: -20 + 8p + 5(-4 + p) + -2(p + 9) = 30 -20 + 8p + (-4 * 5 + p * 5) + -2(p + 9) = 30 -20 + 8p + (-20 + 5p) + -2(p + 9) = 30 Reorder the terms: -20 + 8p + -20 + 5p + -2(9 + p) = 30 -20 + 8p + -20 + 5p + (9 * -2 + p * -2) = 30 -20 + 8p + -20 + 5p + (-18 + -2p) = 30 Reorder the terms: -20 + -20 + -18 + 8p + 5p + -2p = 30 Combine like terms: -20 + -20 = -40 -40 + -18 + 8p + 5p + -2p = 30 Combine like terms: -40 + -18 = -58 -58 + 8p + 5p + -2p = 30 Combine like terms: 8p + 5p = 13p -58 + 13p + -2p = 30 Combine like terms: 13p + -2p = 11p -58 + 11p = 30 Solving -58 + 11p = 30 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + 11p = 30 + 58 Combine like terms: -58 + 58 = 0 0 + 11p = 30 + 58 11p = 30 + 58 Combine like terms: 30 + 58 = 88 11p = 88 Divide each side by '11'. p = 8 Simplifying p = 8
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