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Simplifying 3p + 1 + 8p = 4(p + -6) + 8(p + 2) Reorder the terms: 1 + 3p + 8p = 4(p + -6) + 8(p + 2) Combine like terms: 3p + 8p = 11p 1 + 11p = 4(p + -6) + 8(p + 2) Reorder the terms: 1 + 11p = 4(-6 + p) + 8(p + 2) 1 + 11p = (-6 * 4 + p * 4) + 8(p + 2) 1 + 11p = (-24 + 4p) + 8(p + 2) Reorder the terms: 1 + 11p = -24 + 4p + 8(2 + p) 1 + 11p = -24 + 4p + (2 * 8 + p * 8) 1 + 11p = -24 + 4p + (16 + 8p) Reorder the terms: 1 + 11p = -24 + 16 + 4p + 8p Combine like terms: -24 + 16 = -8 1 + 11p = -8 + 4p + 8p Combine like terms: 4p + 8p = 12p 1 + 11p = -8 + 12p Solving 1 + 11p = -8 + 12p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12p' to each side of the equation. 1 + 11p + -12p = -8 + 12p + -12p Combine like terms: 11p + -12p = -1p 1 + -1p = -8 + 12p + -12p Combine like terms: 12p + -12p = 0 1 + -1p = -8 + 0 1 + -1p = -8 Add '-1' to each side of the equation. 1 + -1 + -1p = -8 + -1 Combine like terms: 1 + -1 = 0 0 + -1p = -8 + -1 -1p = -8 + -1 Combine like terms: -8 + -1 = -9 -1p = -9 Divide each side by '-1'. p = 9 Simplifying p = 9
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