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Simplifying 2p + -3(5 + -2p) = 4(p + -4) + -31 2p + (5 * -3 + -2p * -3) = 4(p + -4) + -31 2p + (-15 + 6p) = 4(p + -4) + -31 Reorder the terms: -15 + 2p + 6p = 4(p + -4) + -31 Combine like terms: 2p + 6p = 8p -15 + 8p = 4(p + -4) + -31 Reorder the terms: -15 + 8p = 4(-4 + p) + -31 -15 + 8p = (-4 * 4 + p * 4) + -31 -15 + 8p = (-16 + 4p) + -31 Reorder the terms: -15 + 8p = -16 + -31 + 4p Combine like terms: -16 + -31 = -47 -15 + 8p = -47 + 4p Solving -15 + 8p = -47 + 4p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4p' to each side of the equation. -15 + 8p + -4p = -47 + 4p + -4p Combine like terms: 8p + -4p = 4p -15 + 4p = -47 + 4p + -4p Combine like terms: 4p + -4p = 0 -15 + 4p = -47 + 0 -15 + 4p = -47 Add '15' to each side of the equation. -15 + 15 + 4p = -47 + 15 Combine like terms: -15 + 15 = 0 0 + 4p = -47 + 15 4p = -47 + 15 Combine like terms: -47 + 15 = -32 4p = -32 Divide each side by '4'. p = -8 Simplifying p = -8
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