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Simplifying -5(4p + 3) + -31 = 3(5p + 8) Reorder the terms: -5(3 + 4p) + -31 = 3(5p + 8) (3 * -5 + 4p * -5) + -31 = 3(5p + 8) (-15 + -20p) + -31 = 3(5p + 8) Reorder the terms: -15 + -31 + -20p = 3(5p + 8) Combine like terms: -15 + -31 = -46 -46 + -20p = 3(5p + 8) Reorder the terms: -46 + -20p = 3(8 + 5p) -46 + -20p = (8 * 3 + 5p * 3) -46 + -20p = (24 + 15p) Solving -46 + -20p = 24 + 15p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-15p' to each side of the equation. -46 + -20p + -15p = 24 + 15p + -15p Combine like terms: -20p + -15p = -35p -46 + -35p = 24 + 15p + -15p Combine like terms: 15p + -15p = 0 -46 + -35p = 24 + 0 -46 + -35p = 24 Add '46' to each side of the equation. -46 + 46 + -35p = 24 + 46 Combine like terms: -46 + 46 = 0 0 + -35p = 24 + 46 -35p = 24 + 46 Combine like terms: 24 + 46 = 70 -35p = 70 Divide each side by '-35'. p = -2 Simplifying p = -2
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