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Simplifying 6 + -3(2p + 7) + -8 = 8p + -1(5 + -4(3 + -1p)) Reorder the terms: 6 + -3(7 + 2p) + -8 = 8p + -1(5 + -4(3 + -1p)) 6 + (7 * -3 + 2p * -3) + -8 = 8p + -1(5 + -4(3 + -1p)) 6 + (-21 + -6p) + -8 = 8p + -1(5 + -4(3 + -1p)) Reorder the terms: 6 + -21 + -8 + -6p = 8p + -1(5 + -4(3 + -1p)) Combine like terms: 6 + -21 = -15 -15 + -8 + -6p = 8p + -1(5 + -4(3 + -1p)) Combine like terms: -15 + -8 = -23 -23 + -6p = 8p + -1(5 + -4(3 + -1p)) -23 + -6p = 8p + -1(5 + (3 * -4 + -1p * -4)) -23 + -6p = 8p + -1(5 + (-12 + 4p)) Combine like terms: 5 + -12 = -7 -23 + -6p = 8p + -1(-7 + 4p) -23 + -6p = 8p + (-7 * -1 + 4p * -1) -23 + -6p = 8p + (7 + -4p) Reorder the terms: -23 + -6p = 7 + 8p + -4p Combine like terms: 8p + -4p = 4p -23 + -6p = 7 + 4p Solving -23 + -6p = 7 + 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. -23 + -6p + -4p = 7 + 4p + -4p Combine like terms: -6p + -4p = -10p -23 + -10p = 7 + 4p + -4p Combine like terms: 4p + -4p = 0 -23 + -10p = 7 + 0 -23 + -10p = 7 Add '23' to each side of the equation. -23 + 23 + -10p = 7 + 23 Combine like terms: -23 + 23 = 0 0 + -10p = 7 + 23 -10p = 7 + 23 Combine like terms: 7 + 23 = 30 -10p = 30 Divide each side by '-10'. p = -3 Simplifying p = -3
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