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Simplifying 3(p + 2) + (p + -5) * 4 = 2(5p + -4) + 4(-1 + -1p) Reorder the terms: 3(2 + p) + (p + -5) * 4 = 2(5p + -4) + 4(-1 + -1p) (2 * 3 + p * 3) + (p + -5) * 4 = 2(5p + -4) + 4(-1 + -1p) (6 + 3p) + (p + -5) * 4 = 2(5p + -4) + 4(-1 + -1p) Reorder the terms: 6 + 3p + (-5 + p) * 4 = 2(5p + -4) + 4(-1 + -1p) Reorder the terms for easier multiplication: 6 + 3p + 4(-5 + p) = 2(5p + -4) + 4(-1 + -1p) 6 + 3p + (-5 * 4 + p * 4) = 2(5p + -4) + 4(-1 + -1p) 6 + 3p + (-20 + 4p) = 2(5p + -4) + 4(-1 + -1p) Reorder the terms: 6 + -20 + 3p + 4p = 2(5p + -4) + 4(-1 + -1p) Combine like terms: 6 + -20 = -14 -14 + 3p + 4p = 2(5p + -4) + 4(-1 + -1p) Combine like terms: 3p + 4p = 7p -14 + 7p = 2(5p + -4) + 4(-1 + -1p) Reorder the terms: -14 + 7p = 2(-4 + 5p) + 4(-1 + -1p) -14 + 7p = (-4 * 2 + 5p * 2) + 4(-1 + -1p) -14 + 7p = (-8 + 10p) + 4(-1 + -1p) -14 + 7p = -8 + 10p + (-1 * 4 + -1p * 4) -14 + 7p = -8 + 10p + (-4 + -4p) Reorder the terms: -14 + 7p = -8 + -4 + 10p + -4p Combine like terms: -8 + -4 = -12 -14 + 7p = -12 + 10p + -4p Combine like terms: 10p + -4p = 6p -14 + 7p = -12 + 6p Solving -14 + 7p = -12 + 6p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-6p' to each side of the equation. -14 + 7p + -6p = -12 + 6p + -6p Combine like terms: 7p + -6p = 1p -14 + 1p = -12 + 6p + -6p Combine like terms: 6p + -6p = 0 -14 + 1p = -12 + 0 -14 + 1p = -12 Add '14' to each side of the equation. -14 + 14 + 1p = -12 + 14 Combine like terms: -14 + 14 = 0 0 + 1p = -12 + 14 1p = -12 + 14 Combine like terms: -12 + 14 = 2 1p = 2 Divide each side by '1'. p = 2 Simplifying p = 2
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