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Simplifying 3 + -1(5p + -1) + -2(1 + 3p) = 1 + -6p + -4p Reorder the terms: 3 + -1(-1 + 5p) + -2(1 + 3p) = 1 + -6p + -4p 3 + (-1 * -1 + 5p * -1) + -2(1 + 3p) = 1 + -6p + -4p 3 + (1 + -5p) + -2(1 + 3p) = 1 + -6p + -4p 3 + 1 + -5p + (1 * -2 + 3p * -2) = 1 + -6p + -4p 3 + 1 + -5p + (-2 + -6p) = 1 + -6p + -4p Reorder the terms: 3 + 1 + -2 + -5p + -6p = 1 + -6p + -4p Combine like terms: 3 + 1 = 4 4 + -2 + -5p + -6p = 1 + -6p + -4p Combine like terms: 4 + -2 = 2 2 + -5p + -6p = 1 + -6p + -4p Combine like terms: -5p + -6p = -11p 2 + -11p = 1 + -6p + -4p Combine like terms: -6p + -4p = -10p 2 + -11p = 1 + -10p Solving 2 + -11p = 1 + -10p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10p' to each side of the equation. 2 + -11p + 10p = 1 + -10p + 10p Combine like terms: -11p + 10p = -1p 2 + -1p = 1 + -10p + 10p Combine like terms: -10p + 10p = 0 2 + -1p = 1 + 0 2 + -1p = 1 Add '-2' to each side of the equation. 2 + -2 + -1p = 1 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 1 + -2 -1p = 1 + -2 Combine like terms: 1 + -2 = -1 -1p = -1 Divide each side by '-1'. p = 1 Simplifying p = 1
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