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Simplifying 3 + -2p + 1 + 8p = 3(8p + -4) + -2(4 + -3p) Reorder the terms: 3 + 1 + -2p + 8p = 3(8p + -4) + -2(4 + -3p) Combine like terms: 3 + 1 = 4 4 + -2p + 8p = 3(8p + -4) + -2(4 + -3p) Combine like terms: -2p + 8p = 6p 4 + 6p = 3(8p + -4) + -2(4 + -3p) Reorder the terms: 4 + 6p = 3(-4 + 8p) + -2(4 + -3p) 4 + 6p = (-4 * 3 + 8p * 3) + -2(4 + -3p) 4 + 6p = (-12 + 24p) + -2(4 + -3p) 4 + 6p = -12 + 24p + (4 * -2 + -3p * -2) 4 + 6p = -12 + 24p + (-8 + 6p) Reorder the terms: 4 + 6p = -12 + -8 + 24p + 6p Combine like terms: -12 + -8 = -20 4 + 6p = -20 + 24p + 6p Combine like terms: 24p + 6p = 30p 4 + 6p = -20 + 30p Solving 4 + 6p = -20 + 30p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-30p' to each side of the equation. 4 + 6p + -30p = -20 + 30p + -30p Combine like terms: 6p + -30p = -24p 4 + -24p = -20 + 30p + -30p Combine like terms: 30p + -30p = 0 4 + -24p = -20 + 0 4 + -24p = -20 Add '-4' to each side of the equation. 4 + -4 + -24p = -20 + -4 Combine like terms: 4 + -4 = 0 0 + -24p = -20 + -4 -24p = -20 + -4 Combine like terms: -20 + -4 = -24 -24p = -24 Divide each side by '-24'. p = 1 Simplifying p = 1
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